Where your rebuilding this XP computer as a spare, you may not know what was previously installed on it?
What I would do is uninstall QuickTime.
Then go to C:\WINDOWS\system32 and delete QuickTime qts - QuickTime qtx - Indeo4 qtx - QuickTime DIR
If there's a K-Lite codec pack installed on the computer delete that also.
Install Windows CleanUp Utility 7.2 run it and remove anything you find related to QuickTime and iTunes.
Here's the link for it > http://www.majorgeeks.com/Windows_Installer_CleanUp_Utility_d4459.html
Now try to install a new QT