Yet - as you said, Ebay survived rather than succeeded. HP is a whole different kettle of fish - beset by rabid competitors on all side and without any significant advantages over any of them. At this stage, Whitman seems a really poor choice who will be immediately out of her depth in running HP.
The core essence of the HP Way consists of five fundamental precepts.
1) The Hewlett-Packard company exists to make a technical contribution, and should only pursue opportunities consistent with this purpose;
2) The Hewlett-Packard company demands of itself and its people superior performance—profitable growth is both a means and a measure of enduring success;
3) The Hewlett-Packard company believes the best results come when you get the right people, trust them, give them freedom to find the best path to achieve objectives, and let them share in the rewards their work makes possible;
4) The Hewlett-Packard company has a responsibility to contribute directly to the well-being of the communities in which its operates;
5) Integrity, period.
So who did you pick? I'm drawing a blank..
The big thing HP was (is) lacking is a leader with experience manufacturing physical products. Putting that in place would settle some of the fears of procurement managers the world over (and maybe settle the stock market too). These aren't the only companies with experience, but it's one place to look.
However, were I on the search committee, I'd look internally first. A junior executive who knows the company might already have the respect of the employees.
Given carte blanche, I'd remove the Board and most of the senior staff.
Actually on second thoughts I'm thinking Balmer. At least MS employees would be happy...
Someone with experience at a product company, that had to oversee design, manufacturing, and logistics. (Ebay is clearly not this.) Also, someone with experience at a services company with a track record of success. (Despite service--and SaaS--experience, Ebay "survived" rather than "succeeded", and in my judgement is not this either.) Someone who doesn't look to acquisitions as a primary way to expand the company's strategy. (Skype is evidence Ebay isn't this.) Someone who can communicate effectively with both the public and internal stakeholder. (A failed gubernatorial bid suggests few people were buying what Whitman was selling.)
In every relevant category, Whitman doesn't make the cut.