Hello, I’m Nathan, and I’ll be assisting you today. My livelihood depends on your positive feedback, so your satisfaction is my highest priority.
Sorry to hear you’re having trouble, Harvey.
This type of problem is often caused by a contaminated laser lens. You've already done the first cleaning step that I'd suggest. Next you can try a specialty cleaning disc (Allsop 23321 Ultra Pro Carbon-Edge DVD and CD-Drive Cleaner) which has little brushes that clean the lens more thoroughly. You can also swab the lens gently with a qtip that is lightly moistened with rubbing alcohol.
If neither of these cleaning steps help, then this is more likely a hardware fault, which could include a bad laser emitter or pickup, faulty spindle motor or laser transport, bad d/a converter, etc. Any of these issues would require repair/replacement. That type of fault is common to see with normal age related wear and tear, as this is a 15+ year old model.
There is a repair service available to do a flat rate repair on this model for $300, and as an alternative you could instead consider hooking up an external cd player to it.
Let me know the results, and I'll advise further, if needed.