Obvious question, but were both PCs running Windows XP?
Did you get offered SP3 via Windows Update on both computers or were you doing it via a CD or "stand alone" file?
Try turning off your Anti virus and firewall before trying to install it again.
Microsoft have a help page here, see if anything there helps
http://technet.microsoft.com/en-us/windows/bb7 94714.aspx
This document here tells you what to do before installing SP3. Note it says to tuen off your anti virus.
http://technet.microsoft.com/en-gb/library/cc1 64204.aspx