"Any suggestions at this point would be helpful."
Read post #3 again.
My guess is there is no "easy-cheap" way to get the Time Machine partition back. "Do-it-yourself" file recovery (i.e., "Data Rescue" or "Stellar Phoenix Data Recovery") may work, but they're not free, and there is a "learning curve".
If the second partition with the music MOUNTS for you, get that second drive up and copy over EVERYTHING from the second partition right away.
I'd write off the data on the TM partition. A backup is really not a whole lot more than a "copy" of what's on your "main" hard drive, and can be quickly reproduced on another [working] volume, in any case.
As I advised above, I'd write off _Time Machine_, too. Yours is but one more in a continuing saga of postings I've seen from folks who suddenly can't access Time Machine volumes/backups/partitions (take your pick).
Download CarbonCopyCloner (it's free). Use CCC to clone your main hard drive to a backup partition created for that purpose.
No, it's NOT "automatic", like TM. You have to launch it and tell it to run (I'm not sure if CCC can do "sceduled backups" - it might be possible, but I've never bothered). Run CCC once a week, or even once daily, and you'll be protected much better than you would be with TM.
I'm _guessing_ that once you get the files off the second partition on the malfunctioning drive, that it _might_ be possible to re-initialize it. If that's the case - if the problems were due to a corrupted directory and NOT a result of "hardware damage" to the drive itself, it can live a new life. I'd suggest that you use it to maintain a "second copy" of the music/movie files. This way you have those files in TWO places, not just one.