Here is a guide to fix your corrupted Memory Stick (it's not dead, it's CORRUPTED)
You know it's corrupted if when the PSP starts up it accesses the stick, then after a few seconds the access light will simply blink. For some reason the PSP doesn't want to reformat it; it thinks there is no stick inserted.
1- Go to Best Buy, or whatever electronics store
2- Buy a PC Memory Stick-compatible card reader
3- Insert your Memory Stick in the reader
4- Format it using Windows (btw, when you do that, format it using FAT32. You'll squeeze a bit more space out of it)
Blammo. It doesn't die, it gets corrupted. It seems to happen mostly when putting the PSP into sleep mode while playing a rom; my guess is that people are sleeping the PSP while the emulator is accessing the stick for some reason.
Best way for this not to happen is to put the PSP to sleep mode while you are at the rom selector menu (or any other static emulator menu). There are a lot less chances of having Memory Stick accesses while in these menus.
It happened to me yesterday, and that's all it took to get it fixed. Don't freak out, don't go out and buy a new MS, just buy a cheap card reader and you'll be set.