Ivey, if yours does not work with the standard Singer cord (I used the one from my FW as that was handy) then I'd guess that someone messed up the wiring inside the machine - and then swapped ends on the power/foot cords to try to get it to work. With mine, the ends are not molded and can be taken apart and rewired. I'm sure that can be done, it's just moving around which wires connect to what pins in the machine.
While I have not yet encountered that on a sewing machine - I've seen it a lot with trailers - it's real fun when you rent a trailer and have the brakes lock up when you turn on your lights . . . btw - we knew our truck was wired correctly, and the time we rented the trailer before it worked fine. Upon inspection - we could see someone had cut the trailer wires and spliced them back together.