Gaming PSP shuts off randomly

[DS1]

the past few days the PSP has been randomly going to a black screen (as in shutting off), but the little green/orange power light flickers a little. I just flip the switch and the PSP starts up again. It doesn't give me the grey 'battery has run out' signal either, it just shuts off instantly without warning.

I can play fine when it's not plugged in (albiet only for 10 minutes, if people will remember my battery issue), but when I plug it in (sometimes the INSTANT I plug it in) it will do the auto-shutdown thing I mentioned above.

So if anyone knows the cause of this, or has tips on what to look for when you open a PSP up (which is what I'm going to do considering the thing is almost useless between the power cord problem and the battery problem) I would appreciate it.

EDIT: I can't even open the PSP up because one of the screws (the one nearest the power port) won't come loose. Probably a good thing considering I don't even know what the problem is.

 

[DS1]

OK I've been experimenting for a few days and I've narrowed the problem down to this: there is something funky with the power port. If I squeeze the bottom right of the PSP (where the battery is), it will shut down. I solved that problem by sticking a piece of paper behind the battery (so it doesn't make contact with the little exposed bit of the power port.

Next, if the AC adapter cord so much as moves while it's plugged in, it shuts down. Some times are better than others (like it can rotate a full 200-or-so degrees before shutting off), but other times the slightest provocation will cause it to shut off.

Some other useful info: If the battery is IN and it shuts off, the battery light will stay on. If it shuts down and the cord is OUT, or the cord is IN and the battery is OUT, the light will shut off. Either way, it is a complete shutdown, exactly the same as a brick is described (except the system turns on just fine). If I make a change to the system settings with the buttons on the PSP (such as brightness or volume) and it shuts down, the brightness and volume will go back to the way they were before it shut down.