Recover & use files from crashed TM harddrive

do you have access to your old computer? you should be able to get your stuff off it without doing uncertain data recovery on a crashed TM drive.
other than that your only hope is data recovery software. I'm not familiar with AppleXsoft File Recover but you can try Data Rescue 3 or Filesalvage.
however, anything they might recover will not be in a nice form and you'll have to sift through a lot of folders looking for various data.

OG-C wrote:
I understand that I would be in a different position if I had my old computer. I don't... And the software I use is less of a problem at the moment.

I'll clarify my question:
Once I rescue/recover all the folders within the TimeMachine structure, can I somehow rebuild this to a disk that the computer will recognise as a TimeMachine backup?

no way. you might recover it using data recovery software but it won't be in any form that TM will recognize as legit TM backups.

V.K. ("the guru" here) is, of course, correct.

Time Machine does incremental backups of new and changed items since the previous backup, but each backup is, in effect, a full one.

This "magic" is done by linking to the backups of the items that did not change with "hard links." An item that was present on your Mac for two or more backups will have multiple hard links to it's backup copies. This structure is used not only at the file level, but also at the directory level.

Prior to Leopard, even OSX did not support doing this at the directory level; and even the Leopard Finder couldn't copy good backups properly, much less corrupted or partial ones.

A data recovery app may be able to recover some of the backup files; but not the structure of links. At best, you're going to get a whole passel of "loose" files, with no structure whatever.

For more details: http://www.appleinsider.com/articles/07/10/12/roadto_mac_os_x_leopard_timemachine.html
and: http://arstechnica.com/apple/reviews/2007/10/mac-os-x-10-5.ars/14