Why doesn't my compressure turn on outside

Bad thermostat, breaker off, low freon /the list goes on.

Does the outside fan go on?

You will need to use a meter to find out the problem. The two thermostat low voltage wires going to outside unit carry 24 volts to the coil on contactor to pull in main relay. The control wires are in a brown covered sheath with two or three wires in it that are about 22 gauge. Trace that to the contactor after turning off power to outside unit. When you find it, and inside unit is on and calling for AC, put leads of volt meter on each prong where wires attach and you should read 24-30 volts. If not, your problem is on the inside. If so, you may have a bad contactor. Turn off inside unit and remove wires from low voltage and read the coil with an ohm meter where you should read around 1000 ohms, if open, it's bad.

Here in South Central Virginia Ants and Earwigs (Dark brown bug with pinchers on its tail) will get in the units contactor points and prevents flow of voltage to compressor and fan motors.

That's a good point. The same thing happens in Florida with ants. If insects get on the contacts the contactor will pull in but no electricity will flow and nothing will run.