does your ac have and refrigerant in it? too little or too much pressure can cause it not to engage... also see if the I think two or three pigtails/sensors associated with the hvac are plugged in and working. (should be temp, pressure, and compressor)
for your fan problems, if you want them to turn on manually www.shbox.com
has a writeup of how to wire in a switch to turn them on as needed.