Hi!
When you press and hold the "R" button, it should load the recovery menu (IF it's modded). So, the PSP isn't modded or it is broken.
It could be a lot of things to be honest. Did you contacted the seller on Ebay and explained to him? Best thing is to return it whenever it's possible.
Otherwise you do need to disassemble the device and check if everything is connected properly and check if all the ribbon cables are fine. Also check the UMD drive and the laser. If all looks fine, then you do need to inspect the motherboard and do some measurement to see what failed...