Thanks for confirming.
That is not an issue with the lens that cleaning can help, it is a defect in the transport mechanism. There is no "fix" for that, as this is a 14 year old model, there are no parts available for it, and it would cost you $150+ to have it repaired at the component level. You could buy a brand new portable cd player for a fraction of that, which is really the only practical option here.
I can recommend some replacements if you'd like though.
Best regards, ***** ***** for the news,
I am an independent technician and I've spent my personal time, unpaid, in an effort to assist with the question for which you solicited my services. This site works on the honor system, and to that end, I have prioritized working with you ahead of other paying customers.
I am only paid for my efforts when customers such as yourself leave positive feedback for my work. Again I apologize there is not a better outcome here, though this is really beyond either of our control. I do hope you’ll consider leaving a positive rating for me, rather than “shoot the messenger”, so that I may get credit for my time spent in good faith to answer your question accurately.