DVD player "cannot play disc". Can I repair that?

I have had 2 players go bad on me. Both have the same symptom. They work fine until all of a sudden when I load a DVD into the player, they can't read them. I tried different discs, tried cleaning the discs, but to no avail. I can hear the disc spin, but after about 30 seconds the display reads "cannot play disc". I tried loading a DVD cleaning disc, but it's the same there - it won't start to play.

Is there anything I can do to fix my player(s)? One is a Sony DVP-NS315 and the other a Philips DVP 3040.