We have occassionally heard feedback that Inquisit does not work with particular joysticks. We've done most of our testing with the Microsoft Sidewinder joystick, so if you have access to one of those, you might try it.
Otherwise, if you are willing to mail us the joystick you are using, we can investigate the problem and, if possible, provide a fix. Of course, we'd send your joystick back to you. Just email firstname.lastname@example.org if you would like to arrange this.