I used a Nikon D5100 with under 2000 shutter actuations. The rear amber light stays on and says to set the date and time but they won't set. The OK button is non-functional. The camera takes a picture but there is no live view when inserting a known good, charged, Nikon-approved battery. There is no green confirmation light. I can't get into the menu. Help. Is it possible I have bad firmware or or a bad motherboard?
If it takes pictures, it isn't a power problem (unless it's a bad power wire internally), which is to say that the battery is likely a red herring.
If that particular camera model has a secondary backup battery, you might try removing and replacing that, just in case this is caused by some corrupted settings somewhere. The indication that the time isn't set suggests that this is a possibility.
With that said, my money would be on a bad cable that connects the display panel and buttons to the main board (and, possibly, connects the backup battery to the main board). If it were just the screen, I'd blame the cable where it runs through the hinge on the articulated screen, because that's a spot where cables often break in various devices, but the OK button (and menu button) points towards a problem within the body itself rather than within the hinge (which is good; cables inside the body are likely to be easier to repair).
I'm assuming that the back panel controls and the articulated screen have at least one cable in common somewhere. If not, then it's probably a defective main board.
That said, I've never cracked open any Nikon, much less that model, so this is all pure speculation based on my knowledge of electronics in general.
Either way, if removing and reinstalling the backup battery doesn't fix it, then unless you're very comfortable doing electronics repair, I would strongly suggest contacting Nikon and getting them to figure out what's wrong. :-)
I'm assuming, of course, that this didn't happen right after a firmware update. If it did, the new firmware is probably a dud. However, if you've been shooting for some time since you last updated its firmware, that's unlikely to be the issue. I have no idea if it is possible to reflash a camera without functioning buttons, so if that's the problem, good luck. :-)