Found the problem.
When I was running the game with opengl settings, it wouldn't let me open up the keymapper. Thanks for the help though! I tried that but I could not get the program to work as I liked.

I have the same joystick and I found that when running the DOSBOX versions of the game, I couldn't get the Logitech profile to activate. The solution is to go into the Logitech joystick software and search for the option to have a profile active all the time (I think it's called a persistent profile or something). You'll have to deactivate that option anytime you switch games or if you don't want accidental presses of the joystick outside of it, but it works much better. I also prefer the customization of the Logitech software; for instance I can program a single button to hit 'S' three times to rebalance my shields. Can't do that with the DOSBOX configuration.