I had four iPhone 4's in a row that all died due to faulty home buttons. I think Apple got cheap in an effort to increase profit. As small as a difference in price as it would be, when you calculate millions of phones it ads up.
My 3GS on the other hand was perfect from beginning to end.
Unfortunately you are either going to have to have it repaired or buy a new iPhone. I wish I could endorse the iPhone 4S, but it has the same crappy button. Mine is already acting up. If only Apple would get with the times and use a touch sensitive button instead of a dreadful old school mechanical button.
I really wonder what the heck they were thinking.