I had a hard drive failure but backed up the data before it was fixed. When I put the data back on, Office would not work. Is there anyway to find the code from the back up data ?
How did you back up the data? Unless it was a drive image which you can restore, it's extremely unlikely. I believe this information is stored somewhere in the registry.
We use Magical Jelly Bean Key Finder at the shop to grab the key before a wipe, but it's not possible from the backup data itself (unless you have mad skills on mounting the registry files).
Now the obvious question: why not reuse the code you have from when you first installed it?