Is there any way to get Jedi Outcast working on windows 10?

Did you already try to set the game to run in compatibility mode for "Windows XP"?

Anyway if you are using an Intel graphic card, you may need to replace the opengl32.dll file with the one provided by GLDirect.

Yes, I have tried both of these methods. Running Jedi Academy for Windows XP worked, but with Outcast I just get a blank main menu devoid of text for new game, load game and so on, as well as the spinning Jedi Knight logo. With the other method, the text appears, but the jedi knight logo is over to the right more than it should be, and as soon as I click to interact with any option, the game crashes. Whenever it crashes, it also SUPER screws up the color settings of my computer.

I was able to get it work by manually adjusting the aspect ratio in the JKconfig.cfg.