98 escort sport problems

okay well i just bought a 98 escort sport but ive got a few issues with it starting hard . ive tried a few things to get it starting better including changing the spark plugs, new battery as last one was origanal, had injectors cleaned professionally, and i also have changed the battery cable ends as they were badly corroded but yet the car still starts hard. now during all this my alternator went out and i had that replaced by the dealership i bought the car from. by the way does anyone know what the average price for an alternator for a 98 escort is because i think i was majorly over charged for mine. um i also appear to have a short in the defrost button for the rear window because when that was turned on thats when the alternator went out and now when ever you push it if you listen to the engine and watch the tach the car starts to idle lower and almost sounds like its missing. Also now my cigarette lighter quit working. so anyway im trying to figure out what exactly to do im gonna start by changing the button for the rear defrost and see if that makes a difference but if anyone has any ideas on the starting hard issue id be glad to hear any suggestions because other then changing the wires which im gonna do this week i really dont know what to try next.

the rpm dropping is the Air compressor kicking on, its will lower the idle and make the car run rougher, that the same on all 4bangers

for the rear defrost?

for the rear defrost? glasser3 = you said rear window defrost button. do you have electric rear window defrost grids in the rear window itself. or you referring to a defrost system of blowing air from the front dash up over your head to reach the rear window as some cars without electric option recommend? if you have electric rear window defroster your a/c compressor would not kick-in.