Well before doing anything with the phone, I would first make sure if it is still under warranty. If it is, anything you do to the phone (outside normal use) could void that warranty. In this case you would want to contact your service provider and/or the manufacturer to see if they can repair or replace it. If however it is out of warranty, then you don't have to worry about this.
First, I would try removing the Battery, Sim and SD card. Leave them out for a few minutes, then place them back in the phone and restart it. This may resolve your problem, at least temporarily
In the end, it could be a few issues. Your screen could be dying (it happens, even without direct damage), you could have loose connections inside the device, which...