I thought my PSP just stopped reading disks one day. I only had two games and they both stopped working. DO NOT THINK IT'S YOUR PSP RIGHT AWAY. UMD disks are shit, and they are problems. I was able to fix the two to temporarily work, but only one of the two works for a good amount of time. I have had no problems with the rest of my games now.
So check the UMD before you blame it on the PSP. Maybe buy a new game or a used one, or maybe borrow one to see which one it is.