After trying several times unsuccessfully to repair a stuck "L" button on my PSP, I finally took the time to see what exactly was the issue causing the problem. The original fix, shaving down the "L" button, which seemed to do the trick temporarily, actually was not a fix at all. The real issue lies in buildup of black residue which originates from inside the rubber covering for the trigger contact. Inside the rubber covering is a small black area, and over time, this black stuff rubs off and onto the contacts, causing a failed reading, thus sticking the button in the closed, or on, position.
To fix this issue, first, review your warranty to see if you can get it repaired by a certified service technician. If you find you do not have a current warranty, you can try this, but be warned, this is not for the faint of heart, nor is it for those who have no idea what they are about to do.
You will need a number 0 phillips screwdriver, 2 Q tips, some isopropyl alcohol.
Remove your faceplate, this can be done by simply removing a few screws. You will need a number 0 phillips driver for this stage. Once you have your faceplate removed, locate the faulty trigger button and remove it carefully. Under that button you will find the grey colored rubber cover, remove this completely. Pick up a q-tip, and soak one end in isopropyl alcohol, shake off all excess. Using the wet end of the q-tip, clean the black part inside the rubber grommet, do this fast, and then dry it off with the dry end of the q-tip. If you let the alcohol stay on the rubber piece too long, you risk damaging the rubber. Once done, set that aside. Using a new, dry q-tip, polish the trigger contacts, this is the part that was covered by the gray rubber cover. Polish this until no more black residue comes off on your dry q-tip.
Once you have these steps accomplished, you can now reassemble your PSP, and give it a shot. Your stuck trigger button should work like new again. One thing of note: To return the rubber piece to it's original position can be a challenge, I used a number one standard flat head screw driver to get the cover back onto the inside clip, the other side can simply be clipped back on by hand.
that's pretty much it, I do not recommend this if your under warranty, for that's always the best repair option, but for those of you who do not have a warranty, if you have the patience and the skills, you may be able to pull this off without a hitch. Just be very careful. And DO NOT TOUCH THE SCREEN when the faceplate is off.