I am having this EXACT SAME problem and was wondering if the OP had found a solution.
Last night, my phone - which has never had a problem and which I have never done anything outside factory specs to - made a weird beep and I looked over to see my wallpaper had gone black and the battery needed to be charged - even though it had been at 80% an hour earlier and my home has 3-4 bars all the time.
I didn't pay much attention, hooked up the charger, and let it go. A few hours later, I unplugged the charger, and all I see is a black background, my top bar with the icons for:
sync, location, 3G, 3 bars, full batt & time listed
and SCREEN LOCKED... but nothing happens when I touch the touch screen. (At the time, it was also giving me an odd "no signal" error - which I have NEVER had an issue with and has since gone away.)
When I press the power button, the screen goes black, and won't turn back on, reset, etc. The sync icon never goes away and the battery drains FAST.
I've pulled the battery, recharged a couple times, let it sit all night, and just did a factory reset.
I got through the activation screens perfectly, then as soon as everything was confirmed and it dumped me to the home screen, the touch screen stopped working again. I pulled the battery and rebooted and I'm back to the black background/screen locked screen.
Should I go straight to Verizon or try to pull the sim card and SD card and try to do a factory reset without those?