The type of problem you are experiencing is internal to the CD player; disconnecting the battery or doing anything else external is not likely to have any effect on it.
What you might want to try is to run a CD player cleaner disc through it; if it is a problem caused by a dirty head or pickup, this sometimes helps. CD cleaner discs are available at Wal-mart or any electronics store.
If this does not help, the CD player will need to be removed from the car and sent in to a service center to be repaired. Here is the contact information for one of the larger electronics repair centers that auto dealers and repair shops use for this type of service:
In that case, the unit will have to be removed and sent in to a repair center to be repaired by an electronics technician. This is how car dealerships and mechanics repair this type of problem; this is not something you can fix yourself at home in the driveway (nor can your mechanic even with thousands of dollars of professional equipment to work with).
I provided for you above a link to one of the largest repair centers that professional mechanics and dealerships use for this type of repair; usually they can quote you a repair estimate over the phone if you call them and explain what type of radio you have before you even send it in.
One other option is to purchase a used CD player from a salvage yard, and replace the defective one you have now...