One of my PSP 3000 is doing the same. Personally I didn't bother to fix because of the fact I own another working PSP 3000. Best solution is to just start ripping your UMD ISOs and load them to a memory stick. Not only you eliminate the need for UMDs, you also get faster load times. Look for CFW 6.61 Pro C-2. It has all you need to rip your isos and to play them. Unless your drive completely doesn't want to read the UMDs at all, then just download them I guess.
I have replaced a screen but never a UMD drive however the drive replacement looks much easier than the screen.