Most of the moving parts in a cd mechanism intentionally run without lubrication to keep dust from getting attracted to it and getting gummed up. Oil and grease act like a magnet for dust and dirt particles. VERY few parts (like only 1 or 2) actually require any lubrication at all, and when they do.... they require VERY little.
I believe the issue you have is likely related to someone nonchalantly lubing up parts, and those parts have got gummed up with dirt and grime because of it. extra grease and oil in place where it's not expected can slow things down to the point of not being able to move anymore.
If this is the case, you will have to consult the service manual and do a complete teardown of the unit and thoroughly clean the parts and also lubricate those parts that need it as directed in the manual. It's a somewhat easy task...just a matter of removing a part, washing and installing it. it's just really time consuming.