The OS loader for a G20 and G23 is the same. The same OS works on both machines.
The game loaded and enabled is what determines if the top screen is horizontal or vertical. And won't make the machine fail in any way. It will just display the top image sideways on a machine without a tall top screen. You would still be able to use the ekey to remove the game that displayed sideways on the top display without any problem.
If you plug in only your ekey and the diag key. That's the basic "machine is ok" test. That's why it's a diagnostic key.

If your machine fails to boot with only the ekey and diag key plugged into the two USB ports behind the metal door and it doesn't validate the diag key, but it did before, the machine itself won't cause that. Your diag key has been messed up from being put in a Windows machine. So you'll need to fix or replace the diag key so it validates first to proceed.
Then you can use the diag key to do a total wipe of the machine's RAM, SafeStorage, and drive. And reload the OS to the machine. But until it boots to the diag menu with just the ekey and diag key plugged in. It's hard to do anything further.