I tried to start my car the other day, and it kept clicking. I though maybe a lose cable. Got under the car, tightened the starter cable, everything started. The next day, it did it again. Tried to start a couple times. Battery died. This time, I connected jumper cables to my car, and it started up right away. First try. Almost too perfectly. I turned the car off to get something to drink, and later started it again. Clicking again. I try to jump it again, but this time, it all went to crap. After a few attempts, my car spontaneously continues to start, even after I have removed the key. My jumper cables have a rubber lining near the teeth area. That starts to melt and almost starts smoking on BOTH sides of the cars connected. I quickly remove the jumper cables on both sides and remove the positive cable on the battery in the Mustang. I thought, "Okay must be the battery and the solenoid. Lets eliminate both possibilities." Got the batterty tested. It was bad. Bought a new one. Replaced the solenoid. Connected everything back up, but no power, at all. No headlights, tailights, instrumental panel lights, no starting, zip. I noticed that one of the cables that connect to the right side of the solenoid (the non + battery side, don't know the proper term) had a little corrosion where the cable had been previously mended together. I cut out the bad portion, and put them back together. I took a couple pictures on my cell phone of the wire connection so that I would not make any mistakes putting it back. My car is stuck at my mom's house, and I want to get it back home to continue working on it without towing it if at all possible. Should there be anything else connected to the battery side on the solenoid, other than the battery? I believe there was a small red wire that seemed to run to the lights wiring bundle in the front, but I could be wrong. I am on my way to the store to buy a multimeter. What is the best way to be sure that the solenoid I bought is working or not? The battery is good, I tested it. I reconnected the old solenoid, and there is still no power. I checked all the fuses in the dash, they are fine too. I heard the possibility of a neutral switch problem, but I have no idea what that means. Where else should I use the multimeter to check if power is in the right places? 
