Turns out for both applications, it was the Addins that were causing troubles. To remove the offending Addin, you need to edit the Registry. Here's the process I used.
- Go to Start > Run..., enter regedit, and click OK.
- Go to the following key: HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Office\Word\ Addins.
- Right-click on Addins and select Export. This will let you re-import the keys.
- Delete the individual Addins one at a time, testing each time to find the offending Addin.
- Once you identify the offending Addin, re-import all Addin keys, and delete only the offending Addin.
- File > Import...
- Repeat the process for Excel at HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Office\Excel\ Addins.