Google Nexus 5 :: Why Doesn't Screen Turn On When Hit Power Button

Hitting the power button does not turn the display on. Actually nothing turns the display on. This began happening occasionally, for a few seconds at a time. Then it became a few minutes at a time. Now it is permanent.

What's truly odd is that the phone seems to be completely working otherwise. It rings, alarms go off, indicator lights flash. It connects to my car over bluetooth and if I plug in headphones and hit the play headphones' action button, music starts. If I hold the power button down, every 5s I get a little haptic feedback, and it appears to reboot if I hold power and volume up (or down, I can't recall), so I know the buttons are working.

I even have a suspicion that touchscreen digitizer is working because I think I've dismissed a few notifications by double-tapping (I'm on Lollipop). Also, I swear I have seen very fleeting, very dim views of the unlock screen a few times.

I should also add that I took advantage of Google's recent replacement policy lenience - this is a refurb I've had for a month or two.

I'm contemplating replacing the screen/digitizer on the theory that this is a broken screen. It feels like the backlight is broken. But I'd rather not spend the $$$ and time if the problem is deeper than that.