Search within backup on new pc

Hello, I hope someone would be able to help me restoring a backup. It is
a little different than any previous threads I could find. My laptop HDD
started to slow down due to overheating. I was able to run a backup,
although it took several hours to complete. Shortly afterwards my HDD
failed and I replaced it with a new one. After reinstalling Vista and my
other programs, I tried to locate the last backup on an external hard
drive. I can see the backup and it appears to be the correct size and
content, but when I try to restore it, I can only see two other backups
done about three months earlier. When I try to restore the most current
backup, it gives me an error message, that the file can't be found.
There is one file in particular that I need in the newest backup. Even
if I can somehow search the contents of the latest backup and pull that
file out of it, it would be of tremendous help.
Thank you!


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Boston