Try it in Safe Mode, then in DOS. (Hold CTRL as you boot for the Startup
Menu, or turn it on at "START, Run, MSConfig, Advanced button). In DOS,
CTRL-Alt-Del should reboot.

If it works in one of those modes, then update definitions, & run a
virus check. I guess, first...

"START button, Run, SysEdit".
If the keyboard is mentioned in Config.sys or Autoexec.bat, put a "REM "
in from of that line.

Both ctrl keys stopped working. Pressing ctrl+alt+del does nothing. In
an application such as Word, pressing ctrl+a, types an "a". Since
neither ctrl key works, I don't think the problem is with the keyboard.

Any ideas what's wrong and how to fix it?

Both ctrl keys stopped working. Pressing ctrl+alt+del does nothing. In an
application such as Word, pressing ctrl+a, types an "a". Since neither ctrl key
works, I don't think the problem is with the keyboard.

And this would be why when you haven't mentioned trying another one on your
machine or your's on another machine?

Any ideas what's wrong and how to fix it?

See above for first half of question and below for one possible solution on the
second half.
You could try booting to Safe Mode and removing any all instances of the
keyboard, reboot and windows will redetect/reinstall it.