Not so weird. I had a favourite CD player I had bought new in 1989 or 90 (Sony CDP-670) that started to skip in 2005 after a move. I ended up buying a really nice new Marantz to replace it. However, I kept the old Sony as it had a great Brown and Burr DAC in it and it sounded great otherwise.
Three years ago (2016), having moved a 2nd time, I decided to set up a 2nd stereo in my den and hauled out the old CD Player and thought ’why not try and fix it’. I went and read this excellent resource https://www.repairfaq.org/sam/cdfaq.htm
and tried all the tips and tricks. I concluded after trying everything that either the laser was bad or there was a tiny crack(s) somewhere in the board. Because it had seen high use I gambled on it being the the laser and ordered a new high quality replacement and had a repair guy I trust put it in. He lived in my previous city so had to wait for a visit opportunity to get it fixed. I spent about $80 on the laser and repair. Then I drove the repaired player home (a 5 hour drive) plugged it in and arghh ... still skipping. So I put it away for 2 more years regretting I had even tried to fix it.
Last month with a little more time on my hands I hauled it out again and took it apart. I switched the cart out with one from a working thrift store Sony CDP-470 (lower model with no Brown and Burr DAC) ... but ... it still skipped. So I knew the problem had nothing to do with the cart/new laser. So I switched them back again. What struck me was that the skipping would happen on its own but also if I walked too fast by my CD Player (laminate on a basement floating floor)
So, I went back on line and read this thread. On a whim, after reading your post, I looked at the bottom of my CD player. Guess what? One of the little rubber 1/4 inch thick foot pads was missing from the back left side - probably knocked off during my move in 2005. So I took a pad from the CDP470, glued it on the 670 and ... yep .. you guessed it. CD player works like a champ. I have run it hard for 40 hours or so with no issues. I can also now walk beside it without causing skipping.
So my theory is that with the missing foot pad the plastic chassis was flexing up to a 1/4 inch which was enough to either 1) disrupt the movement of the optical assembly on the track/rails, or 2) flex the circuit board which may or may not have a crack in it I can’t see. The problem would have been made worse by having an EQ placed on it (added weight).
Since discovering this I see other posts complaining about the cheap feet on many CD players and the benefits of isolation products. So I have now ordered some sorbothane isolation circular disc
s. In the future I will also make sure my CD players are kept perfectly level, just like my turntable.
Moral to the story: Sony and many other CD makers used plastic cases/chassis. They bend. This can effect player performance so be sure this is not your problem before you take more drastic repair steps if your CD player starts to stutter, skip and jump backwards to track 1 (the symptoms I had).