pretty common problem, and most likely the flex connector. Could be worse - the phone is almost 3 years old, and we have another one floating around my house, so I can replace it.
Anyway, I opened it up to see if playing with the connector could fix it, but it did not. Then, just for fun I put it back together without the display. I obviously can't hear anything, because the speaker is on the top part, but it can still make calls, and the mic works just fine. Might be possible to use in some embedded system at some point. Did someone say Port-O-Rotary?