The general 30,000 foot view from Seth Godin:
The problem with home page thinking is that it’s a crutch. There’s nothing wrong with an index, nothing wrong with a page for newbies, nothing wrong with a place that makes a first impression when you get the chance to control that encounter. But it’s not your ‘home’. It’s not what the surfer/user wants, and when it doesn’t match, they flee.
You don’t need one home page. You need a hundred or a thousand. And they’re all just as important.
On the practical side? Realize that the reason why no one is happy with your homepage is that you are sending everybody to the same page. Start deep-linking people in, whenever possible.
Send newbies to the index. Send the daily visitors to the news feed. Send the people to whom you sent your last marketing campaign to a page constructed particularly for them.
When someone says “I couldn’t find that from your homepage,” investigate the obvious question: how did they get stuck going to the homepage in the first place?