I just moved into an older townhome and they have a York air conditioning system. It is an older model but I am not sure how old. I turn on the AC and I hear the fans and system kick on but then seconds later the EM heat indicator turns on and the air quits working. Is this a thermostat issue?

It could be a thermostat issue and from what you said that is the first place I would check. It could also be a low voltage feed back from a defective component in the inside air handler/furnace. Make sure the thermostat is not turned to auto if there is a auto selection between heat and cool. Many older thermostats have a HEAT-AUTO-COOL selector setting. Do not confuse this with the ON-AUTO selection for the blower/fan.