NEED HELP! 2001 Ford Mustang 3.8 litre V6 Bad Ground?? (replc'd Battery, and Alternator, runs only on jumper cables)

My wifes 01' Mustang V6 had some electrical issues; during heavy rains, at night with lights, wipers and heat on, the car would stall or drop voltage to near stall. Radio would die.
I replaced the alternator with the proper one. Problem seemed to have subsided for a few days, then returned. Next I purchased a new battery and installed that after cleaning the battery contacts with a wire brush.
Now, the car does not turn over, does not make clicking noise and all lights are off.
To eliminate the idea this may be a battery issue, we jumped the car off of another car and it started right up and ran perfectly...UNTIL we disconnected the jumper cables, then it dies again.
I have been scouring the web trying to find a solution or something worth trying before I make a repair shop out of our complex's parking lot. I need to do this as fast as possible without any unnecessary tinkering, IF possible.
I believe it may be a grounding issue; I am curious if anyone else has any similar experience or knowledge and can point me in the right direction.
ANY TIPS OR HELP ARE GREATLY APPRECIATED
Thank you in advance.
PJ
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On 4/1/2014 2:20 PM, Pliny Herell wrote:

You get an answer here but you really need to goto one of the Mustang web forums to get lots of feed back.
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Look for a failed ground between the engine block and the battery. To test take one jumper cable and connect from the block to the negative terminal.
After you fix that do a very low voltage check betwwen the metal on the radiator and the battery negative terminal any voltag (likly in the mill ivote range is a predictor of an eventul raditor failure. You'll need a light jumper between the radiator the the negative terminal of the battery.
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