Hi John,
Apologize for not replying in a timely manner and sorry to know that you are facing issues using Office365.
Could you please verify if you have the latest version of Visual C++ installed?
I would suggest you to reinstall all version of Visual C++ and check if it helps.
a. Press Start, and type uninstall a program and press Enter.
b. From the list, find Microsoft Visual C++ Redistributable Packages and click on it.
c Right click on it and select ' Uninstall'
d. Restart the computer.
Now, download and install the versions of Microsoft Visual Redistributable Package and check if it helps.
Latest Supported Visual C++ Downloads
http://support.microsoft.com/kb/2019667/en-us
If that does not help, I would also have you check with the network admin who manages theses machines. Domain questions will be better answered on the Windows 7 Category - ITPro
Hope this helps. If you have further queries, we will be happy to help.