Hello all new here and first time post . I recently have been having trouble with my 1965 mustang turning over while the key isn't even turned to the start position . Just started out of the blue the other day after I installed a radiator. It is a 302 w/ T5 transmission, neutral safety switch is wired on this one . I have replaced the battery,starter solenoid , and even unplugged the ignition switch and car still is turning over . I have the negative off the battery but as soon as I touch it the car turns over and as well seems to want to "melt" or leave indentation on the negative post . I don't see where any wires would be an issue regarding the radiator install. Could the starter itself be an issue ? I have had the car a couple of months , starter appears to be newer . I'm running out of ideas , hoping somebody might be able to help on this one !