Need help with Cougar Electrical Problem

I have a 99 Cougar with the V6 engine. Recently my vehicle would not start. I jump started the vehicle and took the vehicle to a auto parts store to have the battery tested. The machine stated that the battery was bad. I had the battery replaced and was able to start the vehicle and drive off. Today I tried to start the vehicle and it was dead. I was able to jump start the vehicle as before, however even after allowing the vehicle to run for approximately 60 minutes, the vehicle would not turn over once the vehicle was turned off. I re jumped the vehicle and pulled the negative terminal from the battery while the vehicle was running, the vehicle continued to run. I also put a volt meter to the loose wire and the positive and read 14vdc. I am sure the alternator is working. Does anyone have any suggestions.

thank you

Bad battery cables
Bad battery

New parts doesn't always mean good parts.

Thanks for the help

I think I might have solved the problem. I had the battery and alternator checked out again today. And wouldn't you know it, the car starts everytime now, the battery was good and the alternator was fine. I think the problem had to do with a potential short in the radio. I pushed on the radio face today and the instrument panel to the radio faded in and out. I then turned off the radio completely. Now the car seems to be doing fine. Not sure if that was the problem, but its not the alternator(thank god) and I am not complaining. Thanks again for all those who tried to guide me through this.

I recently had a similar problem.. i have a 2000 cougar, it not turn over at all with a 2 month old alternator and a brand new battery.. the battery was charged up 100%, the alternator was working properly, but the car would not turn over at all... i tried jumping itthat seemed to fix the problem for about a month. then it happened again, this time it would start with a jump but would quit as soon as i pressed the brake petal.. had it towed to ford, turns out that the main battery harnes was completely corroded away and some of the wiring along the fire wall had corroded.. the entire car was shorting out when i turned the ignition.. the lovely ford dealer wanted 7 hours worth of labor at 70 bucks an hour which totalled 490 bucks and 60 bucks for parts.. i talked them down to 4 hours 3.5 hours of labor and 60 bucks in parts... i hope for your sake this is not the same problem your having with the car...