1982 Ford F150 starting issue...?

I have a 1982 Ford F150 with a 302 V8 and an auto trans. When I go to crank the motor, the only thing I hear is the solenoid chattering. It has a brand new battery (swapped 4 times since February), alternator, starter solenoid, voltage regulator, and a direct-wire push button starter. Ive checked continuity in all power and ground wires relating to the starter circuit and all wires resulted in .000 ohms of resistance. I tried to jump start the battery but ended up melting the jumper cables. Ive also brought in the starter to be tested and it passed. Any other possible ideas???? I need this truck running by tomorrow morning!!!