WHAT VERSION OF OFFICE? (yes I'm shouting!) What version of windows?
Assuming Office 2010 or earlier ...
You can't. Simple. You absolutely have to have your product key.
If you have a computer with Office activated on it, we can provide you with a tool to extract the product key from the HD.
If you bought an online download license (not likely unless you bought the optional "backup" disk), then you may be able to go back to the online store you bought it from, log in with your email address to get the PK.
Is there any chance you have an image copy backup that has Office installed on it. Then you could use the product key extraction tool.