I've tried to re-record the macros and assign various other shortcuts to them, but they will not run. :-(

OK, in that case, try running your Word with absolutely no Add-Ins.
Add-Ins in Microsoft Word
Use the /a switch as shown.
If they then work, the problem is an Add-In.

You can try Safe mode as well, but for that you must have your macros and shortcuts stored in another template and then (1) create a document based on the template or (2) load the template as a global template.

One other thing to try is storing the macros and keyboard shortcuts somewhere other than the normal template as mentioned earlier.