sounds like maybe a software issue? try backing up your data, photos and such, and reset phone to factory/update phone software/both. may help.

if you have a dremmel with the proper head piece (correct terminology?) you can make a clean cut all the way through the screw and use a flathead screwdriver to remove it. just be careful not to harm the board at all. edit: I should clarify, when I say all the way through I mean the top rounded part of the screw of course.

it's possible the digitizer cable isn't connected properly, I'd say unhook the assembly and re-hook it. if that doesn't work, try unplugging the battery from the board, and plug it back in. it's also possible (maybe?) that the digitizer cable got torn during assembly, and it's not always easy to see the tear as the smallest nick in the wrong place can cause it to go bad.