You haven't given us enough information.
Which version (97, 2000, XP, 2003, 2007) of Office is on the old computer?
Is that version of Office an OEM installation (came pre-installed by the
manufacturer of the computer) or retail?
If this is an OEM Office installation then it isn't legitimate to move it to
a new computer. (And the installation discs probably won't function on a
computer with a different BIOS anyway.)
If this is a retail installation, then moving it to the new computer is a
legitimate thing to do. But any version of Office prior to the 2003 version
will probably suffer some minor-to-severe hardships running under Vista --
if, indeed, it can even be installed.
On a couple of test machines here I was able to install Office 2002
Professional (Office XP Pro) under Vista Business. However, several serious
operational issues were encountered, particularly in Outlook.
My personal take is that, if the Office version is older than 2003, it's not
worth it to even try. And Office 2007 is a better match for Vista than Office
2003.