It sounds to me like, coincidentally, your digitizer may have chosen to go bad right after your upgrade to 7.0.4. One thing to try, however, would be to make a backup of the device in iTunes, sign out of Find iPhone, put the phone into DFU Restore, and then connect it to iTunes and let it reset everything on the device. Once that's complete, restore the phone from the backup that you made. You need to be thorough and be certain that you have all of your music and apps synced with iTunes before you put it in DFU...