How effective is a Time Machine backup?
Whoa, that's a way last resort. You don't have a computer problem, you have a Microsoft problem. Move all Microsoft preference files (plist and plist.lockfile) from both ~/Library/Prefences and ~/Library/Preferences/ByHost, and from /Library/Preferences, to the Trash. 

Any Ofice apps in Applications or the whole Microsoft Office folder, move to trash or zip and store in /Users/Shared. Same with Microsoft folder in /Library/Application Support. Start with a clean state. 

Log out, maybe even Restart, and try installing again. Sometimes just getting a fresh copy of  Microsoft AutoUpdate into /Libary/ApplicationSupport/Microsoft/MAU2.0/ gets it all working, along with letting the apps build fresh Preferences--let MAU find and install updates.