I use a standard Xbox 360 Controller, and it works just fine with this game. I don't own a Joystick, so I can't comment there, but have you tried using the Joystick in other games, to see if it works at all? If the Joystick works with other games, there are a few things I know of, that might help, but there pretty generic solutions, so they probably won't work.
Which version of the game are you running? Because the version listed here is v0.13, but there's actually a v0.13a, which contains some bug fixes (which might include your Joystick problem).
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Try running the game as Admin, if you aren't already. Reset your Joystick drivers or check for updates for them. Maybe try plugging it into a different port?
Also, is your Joystick wired? If not, see the above conversations on this page for our ramblings about that. Lastly, it's possible that the game might just not be coded to handle Joysticks? Grimhelm had previously mentioned that the game was coded for standard controllers, so it might be a possibility that he didn't get around to doing the others.
I don't know what else to suggest, other than just googling your Joystick problem, maybe even with your specific model. I'm sure at some point, someone has asked about this problem before and had gotten an answer.