I had an early Sony CDP-2 (mid 80s). I also was having similar issues.
In my standard fashion, I opened up the unit, and took a peek. I discovered that several CDs had been displaced from the tray into the interior of the box, and were interfering with normal function.
Sucker worked for a long time. I eventually got rid of of it, as it had no SPDIF output, when we downsized 10 years ago.
Longer story is that my LP collection, and stereo, was ruined in Hurricane Alicia (1983 Galveston for med school). My non audiophile, yet music lover, wife got me that CD player, as a gift, early in residency (mid 80s). New technology, not a lot of CDs. I am still so proud of her for that gift. I was still rocking a Harmon Kardon receiver, and DIY 3-way speakers (trimmed down cabinets for WAF)