1)Remove the umd disc from the psp console and look and the shiny silver side of the umd disc. Does the silver side of the umd disc have smudges and finger prints on it? If it does, that can be one reason why the psp console is failing to read umd discs. So using a lint free cloth, wipe aways the smudges and finger prints and insert the umd disc back into the psp umd drive. If the umd disc looks scratched, then using toothpaste buff out the scratches.
2)If cleaning the umd disc didn't work, then i suggest that the laser lens in the umd drive is dirty or dusty. After a while, dust and dirt builds up on the laser lens, which can therefore make the umd drive not to read umd discs. So get a ear bud and some rubbing alcohol and gently clean the lens of the laser. Cleaning the laser should resolve most disc error problems.
3)If cleaning the laser didn't work, then the laser inside the umd drive is faulty, so you would need to replace it at this point.