The CD player is about 20 years olda and has worked fine until a few weeks ago. It does not play CD's now. We sprayed it with air to dust it. It worked again. The next time we tried it does not play again.

Dust inside the cd player could be causing problems.
You need to try playing a cleaning cd and follow the instructions that come with it. You can also spray compressed air to clean out the cd portion of the stereo. You can also try unplugging the unit for 20 minutes and then plug it back in. Make sure your cds are clean and not too scratched up. If the unit is under a year old it may still be under warranty. If this does not resolve the issue you may have to have the unit professionally repaired. If the unit is not worth repairing you may need to buy another unit.

I have problems from time to time with my home cd player and clean it with an air spray can used to clean computers, seems to work for me, it's a cheap first step.

Could be some dust or debris in the unit. Also be careful that you are not putting fingermarks near the hole section of each CD you put in, as the CD plays from the centre out.

Have you opened the computer up and checked the fans for dust. As you say, those are clasic overheating symptoms
Use a small brush and a vaccum cleaner, or a can of compressed air(air duster) to clean your pc's fans.

Check for dust on the optical pick-up in the CD player. If you can, blow CLEAN air across it to remove dust.

Take all DVD dics that freezes,get some dish washing soap wash the DVD dics laser surfaces to clean fingers prints, grims,dusts.Should solved this problems.

check the rca cables and spray out all the dust with canned air

Could be the dvd player/lens. The player sucks up dust through the
player's caddy and after a while it won't read discs anymore.
A cd cleaner or a good (gently dosed) blow with compressed air might help.

dirty,clean the optical pick-up?

Maybe the laser is unable to focus on the smaller pits and lands of a DVD disk but can see the relatively large pits and lands from a CD just fine. This may be solved by using a CD/DVD cleaner disk. It's a disk with small brushes on it that attempt to brush dust from the laser's lense. They don't always work but that's what I'd try.