My psp go keeps turning on and off.

When i try listing to music on my psp, it starts turning off and on i trying googleing for a answer to resolve the issue, didnt find one tried taking the battery out and starting it up with the AC cable plugged up, Does the exact same thing and i even tried taking out the memory stick it stays on longer but after that it powers on and off.

NOTES: I Have CFW (Not permanent)

It started doing this last night.

It still turns on and off while charging.

My psp is old i had it for long time (I think i had it for five years)

it even does this when trying to boot into CFW mode.

UPDATE: When I pull the power switch down where all of the buttons on the psp are disabled, it doesn't cut off at all.