First of all, I purchased it from a seller in Hong Kong on ebay for pretty cheap (£85/$170 - "Like New" condition) with 3.52M33 pre-installed.
The short of it is that I updated it to 4.01 M33-2 back when I got it and everything worked fine but recently it's stopped playing certain games on the memory stick, giving me an error message or freezing for a few seconds before resetting. I've attempted updating to 5.00 M33 and M33-3 but that doesn't work as well as a few other things.
When I received it, it seemed to be in perfect condition although for some reason the battery indicator kept fluctuating between full and one bar (which it still does). Whenever I checked how much battery was left in the system settings it would alternate between the proper amount and 16% (at about 1-2 minute intervals). This had no effect on the PSP itself so I ignored it.
I updated the cfw to 3.52 M33-3, to 3.71 M33, to 3.71 M33-4, to 4.01 M33, to 4.01 M33-2 which is what I'm on now. There may have been less steps involved than this, but I made sure to check at least two guides when updating so that I didn't mess it up.
Everything I played worked perfectly fine at that point and continued to work fine for at least a couple of weeks. The first problem I had was when trying to play a Japanese demo (the Prinny one) that had been uploaded cfw compatible on a forum. All that happened was that when I attempted to run the demo, the screen would go black for a few seconds then the PSP would reset. This didn't seem like a big deal so I ignored it.
Likely unrelated but a few days later the charger I got with it stopped working correctly and I gave up on the PSP for a bit as I had no clue what the problem was. I went around my friend's a couple weeks later and used his charger and it worked fine so I ordered a new one.
Now, most of the new games I put on my memory stick won't work, either freezing and resetting at a certain point into the game (always the same point, usually one of the first loading screens) or giving me the error message "The game could not be started. (80020148)" - this includes some older games. Even a game that worked fine before now shows strange glitched lines across the screen frequently.
I've attempted updating the firmware to 5.00 M33(/-3) but it stops at "Starting sce updater. Wait..." and simply stays there until I turn it off. I've tried changing settings in the recovery menu, I've tried formatting the memory stick and I've tried formatting flash1 and resetting settings but nothing seems to help.