Registration query

[Clarry]

I purchased Office 2003 several months ago for installation on a new PC. Have just acquired an additional PC for home use. Can anyone advise whether I can 'legally' install my copy of Office 2003 on my 'new' machine aswell and register it. Or do I need to get yet another copy? As the PCs are both in the home, I am hoping that I can just put it on the additional PC. Tried the MS site but they appeared to want $35 for support. Thank You