I'm having the same problem as the OP. It's not that the controls in-game are unresponsive, they just don't work at all. I can navigate around the main menu with my game pad, but when I open up the gamepad config menu, I can't rebind any buttons. When I start the game, none of the buttons on my gamepad do anything, I have to use the keyboard. If I go back to the main menu, I can navigate around it again. It's very strange and I'm not quite sure what's going on...
By the way, I'm using a PS2 Dual Shock 2 controller connected through a USB adapter. It behaves the same way whether I have analog mode turned on or off.
For what it's worth, I'm using Windows 7 x64. I also just tested it with a USB Xbox 360 controller, and it behaved exactly the same way.
Ok, I figured out my problem. I feel REALLY silly now.
I had another game controller plugged in, a flight stick that I had set off to the side and forgotten about because I don't use it very often. It looks like it was being recognized as the first controller, and I'm guessing the game accepts input from any controller in the main menu, but only the first controller inside the game. After removing the flight stick, my PS2 controller is working fine.