Can y'all help me recover some files?

I've been using a Simpletech 500gb external hard drive to backup my files. The harddrive came with TotalMediaBackUp to backup everything from my OSX Macbook, which I've done 2 or 3 times.. Shortly after the 3rd backup or so, my macbook died (won't turn on). I'm trying to get my files off the harddrive and on to my mom's computer (also a macbook on OS10.3) but I can't see any of them (just the Backup Software) and when I try to use the backup software to "restore" it doesn't show any backups have happened. Is there anyway to get these files back? I'm currently looking into This Total Media Back Up (which is made my ArcSoft) but my dad seems to think it'd be easier to pull out the harddrive from my mac book and try something fancy like that..

It looks like the drive is using about 40gigs or so (even tho all I can see is the software that only looks like it takes less than a gig), so I'm assuming my files are on there, I just can't find them or the restore file.
please help!