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Hello and welcome to Just Answer - My name is ***** ***** I'll be happy to assist you today. There are several potential causes of the problem you described. Could you take a picture of the control board and post it to this chat? That will help me know what color low voltage wires you have hooked up and what pressure switches your system has connected.
Okay, take a look at the 3rd pic posted - the one where the wires enter the outdoor unit. Turn the thermostat off then disconnect the brown and purple wire and connect purple to yellow instead. Then turn the thermostat back on let me know what happens. If the outdoor unit doesn't come on then check voltage between the blue wire (C) and the purple wire (Y).
Did you have a chance to correct the wiring?