IPhone :: Dropped 3G / White Screen / No Visible Cracks

I can really blame this one on the dog. Walking to my desk, phone in hand, excited puppy races along and bounces into me, phone goes flying. Lands face down.Screen is white, and will sometimes flash grey lines when it seems the phone is trying to do something (like reboot). The music that was playing before the drop continued to play after. The touch screen does not seem to respond. The phone rings when people call me, and my alarm that I had set still went off. Itunes recognizes when my phone is plugged into my computer.

I've been doing research for a few hours trying to see if this is something I can fix - I opened it up to re-seat all the connections, and that didn't help (it didn't seem to make things worse either, at least). There are no visible cracks/breaks on the outside (I have not completely dismantled the inside to see from there).

Phone is a week past warranty, and I don't know that this would have been covered anyway. I'm prepared to fix it myself, as long as I have a good idea what I need to buy. Should I be looking at an LCD replacement? A digitizer replacement? Something else? I've read conflicting things on this. Thanks for any help that can be offered.