A Sega Genesis/Megadrive controller can be plugged into the Atari 2600. B is the default fire button. However, there is no alternate for the paddles.
Fixing Software
Warning: The following procedure is advanced, and should not be attempted by anyone that is not comfortable with such repairs. If you get a blank blue screen when you insert a cartridge, search for a screw on the cartridge. Unscrew it, remove whatever is inside, and insert the chip alone into the console. Turn on the console to see if your game runs. If that does not work, reverse the chip so that the front side is in the back. That should work. Put the cartridge back together according to the way you inserted the chip and your game should work.