Open the UMD tray. Is the 'metal' tray loose or flapping and making noise with plastic back covering? If so continue.
1 Open the UMD tray and pull apart the plastic cover cover from the metal tray. The easiest way to do this is to hold the metal tray in the middle and wedge the plastic out from either side.
2 Once you do this you'll notice 2 metal wing-like flaps protruding from the metal tray. You need to pull these flaps up even more as it is these wings which keep the metal tray firm into place.
3. Once you've done this put the tray back together, the metal and the plastic cover.
Hopefully the PSP will now read the UMDs. This is about making better contact between the UMD and the laser. Working again?.... never doubt this piece of technology