Try turning the phone off. When it's off hold volume down, and the power button until a black screen with white text comes up saying you must "hit power to confirm a factory reset" (or something along those lines.
Sync your contacts and use titanium backup pro or similar apps to back up any apps that you are concerned about using (paid apps sometimes have issues with second/third download authorization.)
Once you've done that, proceed to the below.
You'll have to hit power twice, then shortly after that a "progress bar" will show up, and the phone will reboot when completed, then go into the OS.
Once the phone "logs you back in" wait about ten minutes of doing nothing on the phone (to let it build the cache) then restart it.
After that report back whether or not it's working.
It could be faulty hardware, but we'll try a software solution or two first to make sure.