As Paul suggested, try to eliminate items that could be the problem without having to buy new parts. If one of your battery cables is measuring 1 ohm instead of 0.1 ohms that could be an indication of corrosion inside the crimped cable end/s. Recheck that cable's resistance. If it still measures 1 ohm after making sure your ohm-meter leads are first "zeroed" out, then the cable sounds very suspicious. [Short the ohm meter leads together first and adjust the meter's Zero knob until the meter reads zero before you touch the meter leads to the item under test]. Someone mentioned having a cable that had been cleaned and was shiny externally, but green with corrosion on the inside of the terminal end/s.
I looked at the electrical diagram for the engine compartment on your '64 Imperial. It has a starter relay (usually mounted on the fender well near the battery). It has one large wire connected to a large post (the main battery lead going to/from the starter). It has three other terminals on it: one labeled "B"; One labeled "ST"; one labeled "GRD". The terminal labeled "ST" gets 12 volts applied when the key is turned to the start position and the car is in Park or Neutral. The "GRD" terminal is the ground side of the relay coil and must have a good ground connection to the frame ground of the car. When the key is turned to the start position and everything else is working correctly, then the starter relay applies +12 volts to the "B" terminal which is connected to the + side of the starter solenoid. You can bypass the ignition key start circuit by jumping the large battery terminal at the starter relay to the "B" terminal right at the relay. Either clip leads attached to about a no. 12 AWG stranded wire or just use a screwdriver tip to jumper the two terminals together. If the starter can turn the engine over it will do so [again provided that the battery ground is well grounded to the starter ground]. The only thing left would be bad or pitted contacts inside the starter solenoid which is part of the starter assembly. You would have to remove the starter assembly and take the solenoid apart to inspect the contacts there. That is a job probably best left to professional starter rebuilding personnel.
Joe
begin:vcard fn:Joe Strickland n:Strickland;Joe adr;dom:;;1021 Vaughan Lane;Tioga;Texas;76271 email;internet:jwstrick426@xxxxxxxxxx version:2.1 end:vcard