My blu ray external drive quit playing blu ray movies

Have you checked the settings of the drive in computer to make sure that nothing has changed. You can check online for a driver or firmware upopdate.
You also want to make sure that the correct zone is selected for where you live.
You do need a software program to enable the dvd player to play BD discs so has anything been deleted lately and do you still have the install disc that came with the player , that may contain the software needed to play BD.

Yes I still have the disk but when i tried to install it again it wouldn't let me. And i haven't deleted any software to play the BD. All the Blu Ray Disks do is make a noise in the player and then it eventually quits making the noise. And the Blu Ray disk doesn't show up on the computer.

You can look and see what the actual software name anmd brand is and then go to that companies web site and see if there is any free software you can download in addition to what you already have.
I had a similar issue and I did just that and now I can play blue ray discs.

http://powerdvd.en.softonic.com/