Occasionally I have found that the commercial CD disc cleaner CDs don't work on many CD, DVD, Blu-Ray players. Not sure why. Have tried 3 different brands of cleaners.
Also, occasionally the screws in the CD player cases are not standard Philips/Robertson screw heads and require a special screwdriver.
Once inside the case, cleaning the (usually plastic) lens of the reader is easy to do, but caution must be used as you don't want to put it out of alignment. I have also manually realigned old players that were malfunctioning, but can not be sure I got it perfect, just that they then worked on all CDs I tried (CDs and CD-Rs).
Attached some photos and diagrams from my Sony CDP-950 player (built 1988) that helped me get a good, non-functional, player working. This model has excellent Sony circuitry and the Philips legendary TDA1541 DAC. I paid $12 for it at a thrift store many years ago (2010). Never found a reason to upgrade since .