Our game does not support hotswapping. Your controller must be plugged in, and all drivers must be correctly applied and the controller detected by your PC PRIOR to booting BattleBlock Theater.
Additionally, our game will assume that the first device you touch on the Main Menu screen is the one you want to use. If you use a keyboard to select an item on the Main Menu, only your keyboard will respond until you reboot the game or return to the Main Menu!
If this doesn't address your problem, open Big Picture Mode from your Steam client, go to Settings>Controller, and map the buttons manually.