So, a phone was given to me in order to see what's up with it and possibly fix it. I was unable to do so, so I consult you guys for an advice.
When turned off, the phone can be turned on while pressing the power button(duh), however, when the phone is actually booted up, both power button and back button are dysfunctional, while the menu button works properly. The fact that power button works means that this is probably not a hardware issue, and the fact that this issue persists after factory reset means that this is not a probably a bug caused by installed software.
So, what do I do?