Is this a proximity sensor issue?

This is an AT&T phone that has been rooted and runs a custom ROM (Graviton). No warranty.

When I first got it (used) it appeared to run ok. Over a matter of weeks, the phone appeared to turn off randomly, a problem others here have reported. On closer inspection, however, the phone did not turn off, the screen just would not come back on. If I called the phone it would ring (but I could not answer it). I could hook it up to the computer and view my files. Usually I could get it to come back by rebooting the phone, but now even that rarely works. Even if I try to reboot into recovery mode the screen does not come on.

My theory is that the proximity sensor is always on so the screen will never show. Does this theory make any sense? Might I fix this by replacing the proximity sensor?

Yes, I have used compressed air to try and clean it. I even took it apart somewhat (took the midframe off) and cleaned it. There is no screen protector. The phone does not appear to have been dropped.