You might have changed your region more than 5 times. Once it has been changed more than 5 times it will be set to that region until you reset your whole computer. As a good alternative you can use VLC to play your dvds.
Use the link above and follow directions to install it.
No worries. You won't be charged until you accept and fully happy with the answer. I would attempt to make it work with VLC but I can't guarantee it will work.
I'm going to release this question to other experts and see if they have any other ideas.
I don't think it will cost that much for a third party external dvd drive. One thing is that you should buy one that is Mac compatible. most of those drives will only have the eject button and no play or stop
If you have an Apple Store nearby I would suggest them to help you do a hardware check. I honestly don't think it is a hardware issue since it read data disk fine.
I will request JustAnswer to refund your account since I couldn't solve your problem. You don't have to rate anything.