I bought a new computer and installed MS Office 2003. It works fine except
everytime I open EXCEL, the EULA shows up requiring my acceptance. I did this
the first time I opened EXCEL but the EULA continues to pop up on successive
sessions. My old computer's platform was Windows XP and my new platform is
VISTA.

You can stop this behavior by first logging onto your computer as Administrator and then starting the program to "Run as Administrator". To do this you need to Right-Click on the file itself which should be located in "C:\Program Files (x86)\Microsoft Office\OFFICE11\EXCEL.exe" (or WINWORD.exe)

First close any open office applications, then open each one as explained above, click "Accept" on the EULA and then close the program. This should cure the problem.