There's still hope! Need advice on recovering data

This is a follow up from this thread...
http://www.mac-forums.com/forums/apple-notebooks/313131-mbp-2011-crashed-what-now.html

So I have been exploring different options to try and recover my data. I've tried some optional software and when I was scanning my disk, my MBP suddenly recognized my Seagate hard drive. It threw an error that said time machine can't use the drive.

What files do I need to recover before re-formatting my external hard drive which will recover my time machine backups?

There's a backups directory and a lost + found directory.

Tony.

Personally, before I did anything else to your old external drive, I would try copying the Sparse Image (TM Backup File) to a fresh external drive and then try to access the file from TM.