Problems finally fixed; The joystick on both Win 7 and Win 10 computers, which had showed inactive with multiple games, now works fine.
What I did was go to
Logitech and download the
specific drivers for my joystick. With joystick unplugged, started computer, and plugged-in the joystick after computer stabilized. Then installed
Logitech drivers over what Microsoft automatically supplied. Joystick was automatically set to be the device to be used with "old" games, as per "Device manager' settings.
There was another
possible issue. In Device Manager, there were displayed multiple Joysticks, and multiple
Logitech HID devices. I uninstalled all of them (and their software/drivers) prior to starting this process. I am not sure about this, but I had a HP web cam installed, and just out of caution, I unplugged it prior to beginning this process. I'll tinker with it, and see if that cam was related to my problem.
But, so far, so good. Stick works in all games, including EAW, in all computers, after multiple re-starts. No "multiple devices" detected in Device Manager. Even reconfigured the snapviews (inside the in-game "Preferences" section) in GOG/EAW successfully. I did NOT need to alter the EAW INI whatsoever, either in Win 7 or Win 10 computers, to get the game to run OK.. Oddly, the game itself wanted the throttle to be controlled by the "hat switch", but changed that to "Throttle" in the in-game "Preferences" section. If there's problems there, will go into the INI and check things, and adjust the INI as needed.
Now that fundamental joystick issues have been resolved, I am able to move on to other things.
So, sweet success at last! Thank you all for your help, and patience! I am much obliged!