I used to have this same problem with my old Sony DVD player. I made sure the discs weren't scratched or had dust on them, and still they wouldn't play in certain sections. So, just before the two-year warranty was up, I took the player in to be serviced. The technician explained to me that sometimes the laser mechanism needs to be re-aligned. Once he finished -- and it took just a few minutes for him to do this -- I took the player back home, popped in the discs with which the player was having problems, and they played fine. A couple years later, the problem cropped up again.
I mentioned this problem on this forum, and the general consensus was that it must be a player problem, since many people have gone years and years with their players without any such problems. (And after doing an ecoustics.com search on my DVD player model number, I found out that lots of owners of this particular player model had the same problem.)
If the player is still under warranty, take it in, explain the problem, and, if it's the same problem I had, they should be able to fix it pronto. If it's not under warranty, find out how much it would cost to fix it. The cost to fix it might be pretty high, possibly as high as the cost of the player. Buying a new player will likely solve the problem, but that too will be a costly solution.
cheers,
supervij