First try zapping the PRAM. To do this hold down "Apple-option-p-r" key combination during the boot. Wait until you hear the start-up chimes 3 or 4 times, then release the keys.
Next; Try creating a new user profile and see if the drives recognizes CDs from that profile. If problem persists it would be worth backing up; reformatting the HD and starting completely from scratch. If your system disks are DVD this should not be a problem otherwise you may have to set up your computer as a Target drive and use a second similar Mac to read the disks. This is a lot of work, which is one reason we suggest periodic cloning of your HD to an external. If you can go back 2 or 3 months to a known good system you can save the trouble of having to reininstall and update third party applications not to mention all the System and Security Updates.
Next; Try creating a new user profile and see if the drives recognizes CDs from that profile. If problem persists it would be worth backing up; reformatting the HD and starting completely from scratch. If your system disks are DVD this should not be a problem otherwise you may have to set up your computer as a Target drive and use a second similar Mac to read the disks. This is a lot of work, which is one reason we suggest periodic cloning of your HD to an external. If you can go back 2 or 3 months to a known good system you can save the trouble of having to reininstall and update third party applications not to mention all the System and Security Updates.