What is the problem with the CD player Jim ? Difficulties with tracking I'm guessing ?
Repaired a few CD players back in the 90's, interesting work if you have the service data, but ultimately sometimes frustrating when the problem turns out to be a weak laser which you can't (economically) do much about, which is what happened to a lot of them...
Those early units all had manual tracking offset, gain adjustments etc..which modern players don't have. I remember a JVC player we had had a voice coil operated lens for fine adjustment and a belt driven DC motor operated sled for coarse adjustment - so there were two nested feedback loops for radial tracking!
The first feedback loop controlled the horizontal position of the lens, but if that one got too far to the side a second feedback loop pushed the belt driven carriage along to let the lens recenter itself. Radial tracking was usually sensed by two side by side optical sensors straddling the focal point of the lens (sometimes a 4 quadrant sensor) - if the lens was too far to the left or right the signal from the two sensors was imbalanced in amplitude and gave a tracking error signal to correct it. The tracking offset adjustment would let you correctly centre the lens radially to line up with the tracks and the gain adjustment affected the gain of the feedback loops and therefore their stability and ability to lock onto a challenging disc. (Such as one with a slight offset in the centre hole)
Then there was the focus loop, controlled by the "eye" signal, (raw data from the main sensor) which basically adjusted the height/focus of the lens to get the maximum high frequency detail from the eye signal!
(Very much like simplistic video autofocus that adjusts focus to maximise video signal bandwidth and therefore detail) It also had a gain and offset adjustment for its feedback loop.
Initial focus is found by spinning up the disc then sweeping the focal adjustment of the lens up and down through it's full range using a sawtooth drive until an eye signal is recognised then the feedback control loop is switched in to take control from that point. If you deliberately put a disc in upside down so it can't focus you'll see the lens sweep up and down about 5 times before it gives up.
We had a "test" CD that was basically just a scratched CD that was challenging to play - when all the adjustments were right most players would play it, but when they weren't adjusted right, they would skip...a good confirmation that the factory recommended adjustments were indeed doing as expected.
Even when working properly the difference in tracking ability on challenging discs from one model of player to another was huge! Some would play flawlessly a damaged disc that other players wouldn't even recognise...
Another thing you'll find is that a lot of those older players really did not like playing CD-R discs - either not at all, or they would have great difficulty with them as the reflectivity of CD-R's is only about 70% of a commercial disc, so you need a lot of spare headroom in the laser output and sensor sensitivity for them to play. Some models had lots of optical headroom and could thus play them even though they predated the invention of CD-R's, others without much headroom could not!
Different colour CD-R's had different reflectivity as well. If I remember right the silver backed "blue" CD-R's were more reflective than the Green/Gold type and were thus easier to play on old CD players, (our JVC could play the blue ones well but struggled with the green/gold ones...) but unfortunately the blue ones didn't seem to last as well - a lot of the blue CD-R's I burnt in the early 2000's are now flaking away at the edges so the song/data at the edge of the disc is lost...
and I'm not sure I've got the right one yet 
Ours is relatively modern TEAC Reference 300 - but realised it is now nearly 20 years old - we got it before we got married in 2000.... 
