I would also guess that it might be the power button. You can also disassemble the phone yourself and see whether there is anything physically stuck at the power button. iFixit has a guide how to do that (the midframe is exactly the level you need to access the power button).
For me it had been the other way round: The power button would not register any presses anymore. The only solution for me was to have it repared by Fairphone. Hopefully in your case it will be easier to fix.