When I try to start my 94 merc cougar the engine struggles to turn over (and doesn't) and my neg and pos battery leads get hot real fast.

 

Wow sound dangerous, hmm first off I would check to see if all your battery wires are good and the insulation is not worn away and touching metal. If it worked previously and you changed nothing since then have your starter checked if your wires check out. I not sure, you said the car will turn over correct? If not make sure you are your hooked up right, positive to positive, negative to negative, good luck with it.