I have never had a problem with my DVD player

The symptoms you describe all point in the direction of the player's laser power going down.

When this happens, your player will start to develop problems with DVD-R(W), not recognising the TOC (table of content) of a disc and therefore refuse to play it, skip tracks, etc.

Since there is quite a bit of variation in the reflective properties of various discs, your player may work fine with some discs and not so fine - or not at all - with others.

Unless you have the service manual and know how to tweak the laser output - which is a critical thing to do - I fear your player is reaching the end of its life.

Do not try using cleaning discs as these are more likely to cause damage than the clean your player's lens. If you want to have a go at the player's internals, then first read all the useful tips on this site: http://www.repairfaq.org/sam/cdfaq.htm

Good luck.