How many miles? I only ask because, if you're sure the wiring is good, that sounds a lot like a problem I had on another car, and unfortunately it ended up being a seized engine. My thought is the wiring would get hot if the starter can't turn the flywheel. I would try turning the crank by hand from the pulley with a breaker bar (or ratchet with a pipe) on the bolt that holds it in. I think it's a 12 or 13 mm bolt. If it doesn't turn with a little effort then you've got a more serious problem
Also possible you got a bad starter if you bought from a parts store. Not unheard of, especially if it's remanufactured. You might take it off and take it back to wherever you bought it and have them test it.