Phone screen stopped working without dropping

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 when reconnected would resolve the problem, or your firmware could be the issue.

Obviously if it is the screen itself, it would need replacing. If it is a loose connection, you should be able to (if you feel comfortable opening up the device) reconnect anything that is loose. If you choose to open up the device, please be extremely careful that you do not knock anything loose or damage anything. You don't need more problems than you are already having.