Well, by a stroke of luck I came up with a solution.
When I was trying to determine what was wrong I took off the tray again but when I put it back I didn't screw it. When I tested the tray again it worked o_O. I noticed that when the tray opened, the part were the screws are was pushed a little to the side.
So I left the tray screws somewhat loose to allow it a little range of movement and that was it. Of course, that means that eventually the tray will fail completely.
By the way, what's a good site to order PS2 parts? I'm thinking about buying a complete replacement drive (tray + laser assembly). I think that since that is the part with the highest change of failing it wouldn't hurt to have a replacement handy. Maybe I'd buy another PSU too. Either that or a flip top case plus the laser assembly.