Psp Tuns Off By Itself (psp Fat)

Hi guys. I was playing a PSOne game when my PSP turned itself off. I thought it was the battery, so I put in the charger. But when I used it again it was turning itself off again. Now what happens is: I turn it on, it works for 1 minute, then turns off. I turn it on again, works for few seconds. I turn it on again, but nothing happens. So I leave it without the battery for few hours. Then when I turn it on, everything starts again .. (1 minute, few seconds, then does not turn on).. Same seems to be the same using the AC adapter. So, I do not thing that the problem is with the battery pack.
I am using 4.01-33.. Any clue how to fix that ?

mine was having a similar problem
it was my battery,
try running it without the battery, but plugged in
if it doesnt turn itself off, then it IS your battery, just get a new one
if not then its something else i dont know