Disc Drive Repair
Various factors can come into play which may make a disc drive not function correctly. If all else fails, likely you will need to replace the disc drive or opt for an Optical Drive Emulator (ODE).
"Disc tray won't open/close"
If your console has a tray that ejects to allow you to load CDs, ensure that it is fully opening and closing. If it's not, you likely need to reset its gears, clean gunk out of its gears (optionally grease them with dielectric silicone grease), or the drive belt is stretched out and needs to be replaced or boiled to regain its original shape. If it won't open, it can also be the motor wearing out being unable to overcome the magnet above the disc if the drive is empty — so try always keeping a disc in the console. Lastly, check the entire motherboard for trace rot or otherwise damaged traces.
"Disc doesn't spin at all"
For most consoles, there is a small lever or leaf switch that is physically depressed when the lid is closed. When the lid is closed, the console should spin the CD and start to seek. Generally, if the lid is closed and the console doesn't spin at all it can be assumed that either leaf blade switch is broken or the motor is dead. Below is an example of a leaf blade switch on a FM Towns Marty.
Notice the Red Arrows where the lid switch is located
Lid switch area of the disc drive.
Lid Switch Bridged wires. Still needs tape.
Generally, the fix is to either replace the broken switch or remove it and permanently wire the lid switch together so that the console always thinks the drive is closed.
"Disc spins but laser doesn't move"
If your console has a laser on rails that moves into position under the disc, ensure that it is going the full range and ending in a correct position under the disc. If it's not, you can attempt to clean and re-grease the rails with dielectric silicone grease.
"Reads original discs, but not burned discs"
Often times when a laser is going bad, it will lose the ability to read burned discs (such as audio CDs) as original pressed discs are more reflective and easier to read. A pot tweak should bring back it's strength.
"Spins but doesn't load original discs"
Wipe laser lens with isopropyl alcohol and a cotton swab. If it still persists, you can attempt a pot tweak.
Other Issues
Trace Rot
Trace rot or otherwise damaged traces are a possibility. Here are two photos of an example where trace repair would be required.
Damaged Traces. Note the Disc drive connector was carefully removed.
With drive connector on the motherboard. Barely visible.
Bad Capacitors
Leaked, bulging, or just plain dead electrolytic capacitors can cause various issues including the disc drive not working. Look closely for the top bulging or the top/bottom leaking and clean and replace them if the are. Failed capacitors can show no apparent signs of having failed, so it may be worth replacing them to eliminate another factor in troubleshooting