After pulling the carpet back, you'll probably be able to see where the ribbon cable is cracked/broken. By carefully scraping away the plastic insulation and exposing/cleaning the copper, you could probably make a "solder bridge" across the crack with a medium wattage iron and ROSIN core solder. Re-insulate it with a few wraps of tape or that aerosol "rubber in a can" spray. An idea might be to put a length of a wooden paint stir stick on the back side to keep it from flexing at this point again during the tape wrapping.