Why does the UMD driver affect button presses?

No, don't flash the system. What's probably happening is that the flex ribbon for that side has been corrupted/damaged some how. I had to do this for a 3000 system on both sides, the 'L' and 'R' buttons didn't appear to be triggering until I got into a game (God of War for instance) and when I started playing, I could see problems.

Best thing to do is get a replacement 'L' button flex ribbon off eBay (shouldn't be more than $2) and follow only parts of this guide till you get to the ribbon that needs to be replaced: PSP 300xc Motherboard Replacement