If you mean that you have used the product key for the original installation on that computer, then yes there is no problem, you can use the same key again to re-install.
If you had to contact Microsoft the first time to activate the software (depends on Version), you may need to call and activate it again. There should be no problem doing this, just explain the software is being re-installed onto the same computer due to virus infection. If you were previously issued with an activation code and you still have it written down, most likely that activation code will also work again, as it is based on the hardware in your computer, and ensures the software installation is valid for that computer alone.
If you mean the product key has already been used for installation on a different computer, then no, the same key cannot be used to install the software concurrently on two computers. (Edit: with Office, if the EULA for your version allows it, a second copy can be installed on a portable device eg laptop for use by the license holder only when the primary installation is not being used.)
Edited by Platypus, 22 December 2008 - 05:08 PM.