My Passport Ultra not showing up as a drive under MY COMPUTER - Help!

The drive may be corrupt, not removing it properly is a frequent cause. You can try data recovery software Recuva is free.

TestDisk  http://www.cgsecurity.org/wiki/TestDisk might fix it it’s free. If you are thinking about professional recovery then do nothing. Sometimes you can access the data by booting from a Linux Live CD.

Joe