When a DVD won't eject, the most common problem is that the belt that operates the eject mechanism is slipping and not allowing it to eject the DVD. This can be fixed by either using a re-grip solution
on the belt or having the belt replaced. With the cover off (be careful not to touch anything live with power) try to find the motor and belt which operates the DVD loading & eject mechanism. Try moving the belt pulley with your finger to give it a little help and see if it continues on with the operation. If it does, the belt is probably slipping. It takes more effort on the belt & pulley during an eject sequence rather than the a load sequence, so it may load fine but have trouble ejecting. Gravity and the weight of the DVD is why you may not have this problem during a load sequence.
Let me know what you find and we'll go from there.