PSP stopped turning on - blinks green once

So I have a PSP-2008 with some 6.35 CFW, which also has a recovery app. I started it, recovered, and started playing around. All of a sudden it just turned off, and does not turn on again - in fact, when I try to start it, it blinks the green light just once - so I haven't even got a chance to access the ‘R’ button recovery. I've checked it both with and without the battery - same thing. The voltages on the battery and the cord are all correct. What could the problem be?