This is more of a warning as well as a solution for folks.
It seems that the PSP doesn't have battery discharge management software.
What do I mean by this?
A typical PDA, camera, LapTop, Etc.... has software that allows it to charge, but not discharge. Well between working, Total Tech on the PC , and the fact that i've not been playing with it off of the cord, the PSP discharged it's battery. So my solution to anyone that has a problem with it not turning on is quite simple, unplug it for a minute, take out the battery, plug it back in, hold the power up for about 30 seconds. Replace the battery , and let it charge. I though mine had went dead because of this, now it's recharging. Although you'd suspect that it'd charge and stop. It discharged.
A warning and solution brought to you by.
I don't know, and you don't either.