I'm relatively certain this is a hardware issue, but try something relatively basic first: delete the seplugins folder from your PSP and reinstall the CFW from scratch. This will help eliminate the possibility that a rogue plugin is at fault. If that doesn't help, well, unfortunately, it's likely a hardware issue that will only be remedied by actually opening the PSP, figuring out what precisely is wrong with the switch, and replacing pieces as needed.
To note, I had a bit of a lemon of a PSP I bought with the same issue (among others). I never was able to properly diagnose all of its issues, but I was reasonably certain that due to the nonfunctional UMD drive, the PSP had likely been dropped while in sleep and something broke by the power switch.