I know nothing about the LaserActive but I know the Model 1 Sega CDs had a lot of problems with the disc tray mechanism. my guess is your gears are messed up or the O-rings are worn out. no idea.
check the tension on any O-rings or belts if there are any. check for missing or worn teeth on any gears if there are any. capacitors go bad. you need a special tool to be able to check them otherwise a visual inspection works. check for leaks on the tops of them. look for any corrosion on the board that would indicate leaks. if there are batteries on the board, check the voltage. get a DMM and poke and prod around checking for continuity.
it sounds like youve already done most of this but this is what id have checked
check for dirty loose or corroded grounds... find a PCB layout if you can, that will help with finding the problem.. check each component one by one. look for broken traces and check for continuity along the traces