Why won't my camera turn on?

I was just in the middle of taking some photos, when my camera went off. I left it for a while, tried again and then it turned on. But the next day it wouldn't turn on at all. I have a spare battery and made sure both were charged, and tried both. I've removed SD card and lens, nothing. Normally when you remove lens or SD card a light flashes (provided battery is in), and that didn't happen. I've checked the battery contacts and they're clean.
My camera is (was?) a Nikon D3200.

Maybe your battery charger is faulty.
Do you know another D3200 owner who could let you try one of his batteries or loan his charger?

Thanks for your reply, but I can see no reason for it to be faulty (besides, I tried both batteries before they were /fully/ charged)… And no, unfortunately I don't.

The most common cause is a bad charger. I have had Nikon chargers go bad before, even brand new ones.

Recharge battery overnight then try again in the morning without a memory card or a lens. If the camera still fails, bring camera, charger, lens and batteries to the store you bought the camera from and ask for service.