Sorry to be the bearer of bad news but only official and 3rd party controllers work with the Xbox. The problem lies in the Xbox's BIOS being only able to recognize and use certain USB devices that were designed for (you guessed it!
) the XBOX. If you want to use a different controller you can buy an adaptoid which converts the information from one controller (like a PS2 controller) to an Xbox friendly data language. Or you can swap out the internals/rewire the buttons from one controller to another (which I've done and is WAY more work than its worth). Or you can write your own BIOS to work with new USB controllers (has yet to be done).
And while 360 controllers can physically connect to the Original XBOX and they're both USB devices, its not that simple. They are very different in terms of how they are programmed to send and receive data and the "language" they "speak" with the console itself.
Or you could take apart the controller and try and figure out whats wrong with it. Often times I've found a bad cord to be all thats wrong with a broken controller.
good luck, happy modding