When I start up Office 2003, Windows Installer intercepts the command and acts like it wants to install a new program. Then an error message pops up to the effect that it can go no further because another pop-up box is open [i.e. the Windows Installer box]. I hit "ok" and the Windows Installer stops, and Office proceeds to open normally.

This is a frequent problem in Office when U use some cleanup tool it deletes one of the file.Just look into this folder C:\Documents and Settings\All Users\Application Data\Microsoft\Office\Data and check whether the file data.bak is available or not.Either you should repair as mentioned by Vishal or just try to restore your computer, the problem would be solved.I had once read the workaround for this on one site long time back if this doesn't solve the problem then do reply

4 more details on Windows Installer check here

http://msdn.microsoft.com/en-us/library/ms973805.aspx