Google Nest Community

I installed a thermostat that was n ew in the packaging never used before. I have all the correct wirring R Y W G C all test are working fine except ounce you set and turn on the AC to a temperature to 62 the ac runs and runs for hours with no change...

Need Help Determining if I can use a Nest Base Thermastat on this. I have a C wire on the one and don't on another is the less expensive nest thermostat compatability with both these systems?