|"I just purchased this PC from Tiger Direct..."|
Then I'd suspect it's a legitimate version of XP.
" The Office 2007 program I am trying to install had been installed on my previous PC without a problem."
Is it still on the "previous PC". Legally, it's one installation per machine (though that would likely have little to do with your current problem). Is the disc authentic (i.e.---where did you obtain it?)
"Should I try to re-install the XP program from the recovery disk that came with it?"
Not if the XP installation is working properly otherwise. Reinstalling could cause you to lose everything else on the machine---specifically if you reformat during the installation process.
"According to the System Properties, Service Pack 3 is installed."
Then there's really no reason Office 2K7 shouldn't install, other than having problems reading the disc it resides on. Could be a problem with the disc or the drive. Do other discs read properly in the machine? If not, the drive may be at fault.
"Channeling the spirit of jboy..."