If your iPhone has a section of the screen that is not responding to touch, check out this article from the Apple site: http://support.apple.com/kb/TS1827.

You can follow all of the steps they recommend, but if you have a real hardware problem, they probably won't work. The interesting thing is that they will let you bring your iPhone into the Apple store if it has a dead strip on the touch screen *even if* your iPhone is out of warranty.

People have reported that even though their iPhone is out of warranty, if you show up to the store with a verifiable dead strip on the touch screen, they'll replace your iPhone with a new one of the same model (no free 3G upgrade).