Give Yahoo’s board credit for pulling one thing off: Naming Marissa Mayer as CEO has everyone rooting for Yahoo to win again.

The Valley has always had a soft spot for Yahoo, the way it did for Palm. The halo managed to survive Carol Bartz, but it took a thrashing under the patent-trolling, consultant-loving, resume-bolstering, and generally anti-Valley ethos-having Scott Thompson.

But ask well-wishers how Mayer will actually make Yahoo relevant again, and they twist into contortions of attempted positivity that can’t really be backed up with any sense of conviction. It usually ends with a not-too-inspiring, “I hope she can do it…” or “Well, if she can’t, no one can.”

The answer to Yahoo’s woes can’t be merely bolstering the ad business. If the answer were ads and media, the board would have given the job to interim boss Ross Levinsohn, not Mayer. So let’s assume Plan A is out.

Plan B, as articulated by Marc Andreessen on the day Mayer was appointed, was to seriously slash headcount. It’s the harsh reality every recent Yahoo CEO has faced: No one thinks the 18,000 person company is a lean organization. Many recommend a cut as high as 10,000.

But that’s easy to say looking from the numbers. It hasn’t happened yet, because picking 10,000 actual people to fire and dealing with the media and personal fallout of that decision isn’t a role anyone relishes, least of all someone like Mayer, who wants to give out more perks and focus on growth and new products.

Perhaps it’s still too early to judge, but Plan B doesn’t seem to be her solution either.

That only leaves Plan C: Coming up with something new and big to make Yahoo relevant again in the product world where Mayer is so revered. The “easiest” and quickest way to do that would be to buy. Lucky for Mayer, in about a week, she’s getting a big cash horde from Yahoo’s sale of half of its stake in Alibaba — about $4.5 billion. People have already been speculating what the acquisitive executive, who sought to buy properties like Yelp and Foursquare while she was at Google, could be eyeing. And plenty of her VC pals who are so kindly rooting for Yahoo to win, are now gussying up startups for sale that don’t look so hot, post Facebook-IPO.

But I put “easiest” in quotes because while it may be the best shot to turn Yahoo around — not to mention achieve a quick stock bump and a nice headline — there’s not a lot of precedent out there to believe it’ll actually work. Buying a few small properties isn’t going to move the needle on a company this large in either stock price, revenue growth, coolness, or in terms of bringing a fresh wave of new talent into the company all at once.

Instead, Mayer needs to look to the handful of Internet acquisitions that have actually gone well, where the product has continued to grow, and, by-and-large, both the acquirer and the acquired have both benefitted.

Exactly two come to mind:

1. PayPal: My recent griping about eBay’s custodianship of PayPal aside, nearly everyone looks back on this as one of the great acquisitions of the Internet. For just $1.5 billion, eBay not only got a payment system that made its core product a substantially better experience that more people could use, but it now makes up a whopping third of eBay’s annual revenues. Most people expect that PayPal will exceed the core business in the future.

EBay bought PayPal from a position of strength, and it’s been bailing eBay out as it descends into weakness. While eBay has limited PayPal from doing much more than Elon Musk’s 2000 product road map, and there was an immediate and swift exodus of talent, it hasn’t destroyed the product. Nor has an up-and-coming startup…. yet.

The key here was PayPal and eBay were an extraordinarily symbiotic fit. The kind of synergies that M&A groups love to promise, actually occurred in spades.

2. YouTube: Unlike most acquisitions of a surging company with the world ahead of it, I’ve always understood why Google made this deal, and why YouTube took it. Google had a monopoly-money stock price at the time, and it needed another big revenue stream, not desperately, but in the future. Meanwhile, YouTube had very real threats to its surging business, including escalating bandwidth costs and mounting legal worries. Google could easy help with both.

So there wasn’t a lot of reason to hate the deal, but was it a bargain at $1.65 billion? A few years ago, I wasn’t sure. Video has not set the world on fire in terms of ad revenues…for anyone.

But YouTube has long had significant cultural relevance — much like Twitter — and it is suddenly proving an incredibly valuable platform to the startup world. Los Angeles has a crop of up-and-coming companies building huge audiences and businesses on top of YouTube, and there’s a boutique industry dedicated to YouTube search optimization that swears it moves the needle when it comes to sales of beauty and fashion products. YouTube has quietly become one of the biggest search engines on the Web. There’s money in that, and Google is the best partner to help extract it.

But unlike PayPal and eBay, YouTube wasn’t a success because it was so aligned with Google. The fit didn’t make much sense at all, in fact. This was a case of trying to buy the next big growing thing while the market leader still could. It was a Facebook and Instagram move. It was precisely what Yahoo failed to do with Google and with Facebook and what Google failed to do with Twitter, Foursquare, and Groupon. YouTube’s own challenges — and the general uncertainty about Web 2.0 back in 2006 — helped make it happen.

Had Google been a struggling company buying YouTube as a final Hail Mary, it likely wouldn’t have worked. The beauty of this deal was the timing: Google didn’t need for it to turn around a huge profit anytime soon, and so it didn’t strangle what was working about the product, say, cramming YouTube full of ads immediately. More to the point: Google kept its word and let YouTube stay independent. That almost never happens with Web acquisitions. It’s taken six years, but we may just now be seeing the promise of that deal.

It’s hard to think of what that PayPal-like fit might be for Yahoo, because Yahoo doesn’t have a focused business. It is the No. 2 player across a range of products, like mail and search, while the finance and sports verticals mostly rely on aggregation of third-party information, not innovative products.

It’s possible a Zynga could fit in — given Yahoo’s foothold in casual games and middle America demographic. But Zynga CEO Mark Pincus would pretty much have to go back on everything he said at our PandoMonthly for that deal to happen.

Likewise, Yahoo has always struggled to build a more robust local product — as have all of the big portals. Yelp and Groupon are options there. Yelp balked at a Yahoo sale pre-IPO and several CEOs ago. But that might have changed by now. My sense is no one wants to touch Groupon — it’s more radioactive in the markets than Zynga.

A Reddit, if it weren’t owned by Conde Nast, or a BuzzFeed would dramatically update Yahoo news and entertainment, two important verticals. After all, Yahoo founder and former CEO Jerry Yang long called Yahoo the “homepage of the Internet” a moniker that has since been bestowed on Reddit. And BuzzFeed’s strength — according to our own Farhad Manjoo  — is largely repackaging Reddit into a better form. The caveat is that this would take Yahoo further down the media route, which doesn’t seem Mayer’s strength.

Still, none of these have that tight symbiosis PayPal did. I struggle to come up with an analog here.

So, what about buying a YouTube? Well, the timing might be right. While Google took advantage of the uncertainty around Web 2.0 back in 2006, Yahoo could take advantage of post-Facebook-meltdown fears as the trickle down through the ecosystem. I have no doubt companies that wouldn’t have sold a year ago, would consider it now.

But the key with both the PayPal and YouTube acquisitions working was that the products were so unbelievably strong, that even with the founders rapidly leaving, the product didn’t suffer. Likewise, users didn’t care the companies were owned by someone else. The product was so good, corporate parents couldn’t screw them up.

What fits in that lofty camp today?

Well, I’d say it counts out Foursquare. While any corporate Leviathan would be lucky to get Dennis Crowley as a product guy, and he has a good team, it hasn’t yet proven the product is relevant to the masses. The product could still wither in the wrong hands.

Tumblr might be an option, fitting into that camp that wouldn’t have sold a year ago but might now. But the product isn’t quite big enough to move the needle on a company as large as Yahoo. Ditto, Path. (And Dave Morin is even less likely to sell.)

The obvious candidate, if you are talking about a product that just will not die no matter what atomic bomb of ill-suited management you throw at it, is Twitter. That would be the coup of the century. But it would also likely cost more than the entire trove of Alibaba cash, and I don’t see CEO Dick Costolo giving up that quickly. Twitter is far too big to be Yahoo’s YouTube, and a potential humbling is still theoretical.

If Mayer wants to find her YouTube, there’s really only one company that comes to mind: Pinterest. The demographic is right. Pinterest isn’t yet making money, so it’s not as laughable a suggestion as Yahoo buying Twitter. It would take one hell of a price tag, and it’d still be a long shot. Plus if the two got into talks you can bet Facebook — even with a hobbled stock price — would swoop in Instagram-style, as would Microsoft and Google.

But ignore that for a moment, and this seems to be the closest there is to a golden goose that would impress the hell out of the Valley and have a big impact on the stock and the company. And if you buy that Pinterest is the next wave of social networks, it would arguably catapult Yahoo ahead of Facebook, not playing a pathetic game of catch-up. It would get people talking about Yahoo again, casting it in a whole new light — yet at the same time, it wouldn’t be so wildly different from Yahoo’s strengths and audience. Pinterest with its design influence could remake the homepage of the Internet dramatically, and Mayer has enough product ballsiness to defy the Yahoo fiefdoms and let it.

Of course, the key to both the YouTube and PayPal deals was that they were done out of a position of strength on the part of Google and eBay. Expecting something at that level may just be too much to hope for even for a company with the reach and resources of Yahoo and the pedigree and good will of Mayer.

But I’ll tell you this much: If the history of consumer Web acquisitions is any guide, a few piddly deals isn’t going to turn this Titanic around. If an acquisition is her hope for change, it needs to be this audacious to work.