Latitude E7250 won't power on

I was just using it as normal and then it just powered off.

No animation, no powering off text, just straight up died, as if the battery was removed while the computer wasn't plugged in.

I assumed it was just an overheating error, so I let it cool off and turned it on again. This time, the computer turned on, 3-5 seconds later, it powers off, with one of the LEDs blinking.