Hello Sanch welcome to the TF! I know nothing about your NH, but are you sure that the circuit you followed to did not branch off the main start circuit and has just led you to a plug that is unused? I cannot hardly think that a plug came unhooked to cause your problem and you cannot find where it should plug back into. Unless you have had a lot of the wiring in that location disconnected for a repair. Please double check this. A neutral switch or other type of safety item causing an “open” in the start circuit would be a far more likely problem. Any chance rodent damage is your problem?