I've had 3 Carver CD players from the early years (TL3300, DTL-100, DTL-200 MkII) and I've seen a variety of issues. One I was able to get working to about 95% reliability (still skipped every so often) and I gave that one to another member on this site. One I chose to give up on...and scrapped. The last one I have is the one I'm still using DTL 200 MkII. It came relatively new in box a few years ago and works great.
I've learned a few things in playing with these units. 1. The belt drives go bad in some of them. They are little rubber bands that like to deteriorate over time. Check for belt slippage. You can get replacement belts on line for pretty cheap and it's not too bad to fix. 2. There are thin metal rails that the transport moves on perpendicular to the disk grooves. Lubing these rails with a light silicone oil (real light so as not to get goop in any other parts) and cycling through a few complete disk travels can help. Sometimes they get dry or slightly corroded and cause the laser to hang up or stick a little. I've also noticed that the skipping can be more prevalent on a cold start up, which I think is related to this issue. 3. The pickup lens can get dirty. Clean the lens gently with alcohol and a lens cleaning paper.
Those are the "easy" things to do.... and they may help your situation.
If you are still skipping after all that, then you are likely into the transport mechanism and/or a new pickup . I think that's much more difficult repair, so I've never attempted it.
Somewhere on this site is a list of which manufacturers made those Carver CD players. Other than the DTL feature, the CD players were the same design built by other companies for Carver corp to badge as their own. I think one is an AIWA design, I can't remember. Do some searching here. You may be able to find components from the sister units built by the original manufacturers.