I'm having this problem right now as well. This has happened to me twice before, once in June & again in August. Both times was the result of me dropping the phone in the middle of doing something on it. This morning it happened again :-(
The good news: it is fixable, I've done it before. The bad news: I can't seem to replicate how I got it to work in the past. I'm in a position to be much more attentive/scientific in how I test getting it to work again, so if I figure it out I'll post back.
This seems to be a more common issue with the Droid than you'd think. I'm surprised nobody has managed to come up with a definitive solution yet. It seems like it's a software problem, as I've been able to resolve it a couple of times now with no indication of any damage to the actual screen or loss of data once it's working again.