So I had this problem one night, and I fixed it after removing the battery and restarting multiple times, but it happened again and now nothing will fix it. Here's the deal:
During playing Dissidia 012 it felt like I nudged the hold button somehow (not enough to flick off the system or put it in hold mode) and then the PSP reacts like I had pressed the start button (pause menu comes up). At this point I'm no longer able to press the start button anymore, and if I press Home I get the "exit game yes/no" screen but the cursor is not flashing and I cannot press any buttons. After fiddling a bit I realize if I flick the hold switch down into hold mode the cursor will flash (but the lock/key icon pops up and I then can't press any buttons). If I very carefully nudge the hold button out of position without putting the system into sleep mode then I can use the d-pad again to select yes or no and either go back to the game or go to the XMB. Either way, though, once I'm back in game I can't use the start button still and if I press home I'm back to unfunctional home screen with still cursor until I put it in hold and carefully nudge it out again. Now here's the weird part, the sleep mode (flicking the switch upward) effectively acts as the start button now for me. It still puts it to sleep, but when it wakes up it presses start automatically. I've tested this on both Duodecim and Legend of Heroes: A Tear of Vermillion, and it works on both (or all, even, I assume). So I guess I'm not in to much trouble since I have work-arounds for the issues, but man is it strange.
I have a PSP-3000. Never had custom firmware on it, always official, I don't mod my systems. I use Media Go for transfers. I've never had this issue before a couple of nights ago but it has recurred two nights in a row, and despite fixing itself with restarts and such the first time aroudn nothing seems to help this time. Does this sound familiar to anyone? Does anyone have any clue how to fix the issue? Could it be a firmware issue? I remember my start button use to be very easy to accidentally press so it could be a hardware issue I suppose, though it seems to be only effecting the software. Any help appreciated with this very strange problem.
So it turns out I don't even have to go in and out of sleep mode for the start button to activate, I can just flick the hold button down then gently nudge it up and it acts like I pressed the start button too. Somewhat more tolerable since I don't have to waste battery putting it in and out of sleep mode constantly, but I'd really like my start button back still.
After a little research I've discovered this is an issue that has affected a small number of other users. It seems the solution is to replace the home/sleep switch. Not like I'm under warranty on this used PSP, but I think I'll just live with it unless it starts to affect other buttons.