There are LOTS of mechanical parts on a CD player that can age/wear. Does your car run 10 years with zero service needed? And there is also the issue of the laser assembly -- its performance also deteriorates with age and use.
Most of those issues are going to require the attention of a trained technician with access to the needed test equipment. Unless you are really lucky, I doubt its something you can fix with a $15 kit. The one exception to that might be if the CD tray area and laser are dirty. There are cleaning kits you can buy but there's no guarantee that this will fix things.