The only suggestion I would have is using something like Revo Uninstaller (the free version or trial version - either will be fine) or similar to uninstall MS-Office 2013 and then reinstall it again.
Revo removes everything associated with a program, leaving no traces behind.
If that does not solve the problem then I'm stuck as a fresh, completely fresh, install should install all Office programs in working order. I suspect that the standard uninstall leaves some bits behind and that corruption in one of those bits is at the root of your problem.
As another quick suggestion search your machine for the file "winword.exe" and try starting directly from it. If that works then somehow your shortcut is hosed.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1809, Build 17763
Presenting the willfully ignorant with facts is the very definition of casting pearls before swine.
~ Brian Vogel