I have a Touch where the display itself is broken but touch screen functionality still works perfectly fine. In my case it's easy to verify because the lower third of the screen still works. With a completely dead screen you could verify by hooking up USB and see if the PC detects it after touching the screen in the right place (the connect button). On my touch this button is in the center of the screen, about one inch from the bottom.
Touch screen failure can be caused by dirt (outside in the display borders, and inside the device itself). It's also possible that the board itself is not mounted/aligned properly.
Sometimes it's just a failure of the infrared emitters/sensors, I've bought a used Glo with perfect display but no touch whatsoever. I suspect it's the board itself in this case, but I can't test it... haven't had luck on Ebay lately, people just bid too much for broken stuff.
