Log for the root directory of an external HDD I really doubt that this would be possible, but is there any chance that OS X 10.7.5 logs the root directory contents of an external HDD that was plugged in through a USB drive a week ago?

My external HDD died and I would like to retrieve the info of what folders it contained just to know if it worth 800 USD to get it fixed.
Nope, there is no log of such. 

The data, such a spotlight DB, is stored on the drive itself.