Why my Mercury Cougar wont start?

This sounds like your alternator is not charging and your battery is very low from no charge, That would explain the stall when the cables were disconnected! If you get it started check the voltage at the battery (13.8V to 14.7V) to confirm if the vehicle is charging. ADDED: The reason your accessories are haywire is because the GEM (generic control module) is not receiving the proper operating voltage and causing a malfunction with the relay drivers.