This is a typical problem that I have found under Windows 2000. The trick that I have found is that you should not run the default exe the icon points to containing the intro company logo movies. This *always* locks out the keyboard for me when I run it.
Instead, change your shortcut to run the StarfleetOP.exe file. This will bypass the intro logo movies and will also resolve your keyboard lockout issue.
Important Note: If you are creating a new shortcut to point to this file, make absolutely sure you fill in the working directory box with the correct path to your OP directory. Failure to do this will create problems accessing fighters on carriers.