Many good suggestions here... I would agree that it's the risk he took buying on ebay, although I would also be frustrated were I in his shoes.
However, there are a ton of avenues available to him - the first of which is to troubleshoot. It could be the disc he's using, something in the settings, the firmware, his cables, you just never know, but he needs to try all of those before claiming the player is bad. Switch from component to HDMI or vice versa. Change the input on the TV. Try other discs or make sure the player works without a disc, as others have mentioned...
If he's done all of that and it still doesn't work, it's up to you as a seller and how you want to handle it. Did you ask him if the box looked like it was beat up when he got it? That might give some indication that it was a shipping problem and maybe the insurance would cover it. Beyond that, it's going to come down to how important your feedback rating is to you, because you know he'll go to the trouble to toast you for it...
There are so many things that can cause problems with those players, though, that it could just be his ignorance - until you try all of the options to narrow down the problem, you just don't know...