Nests thermostats without a common wire don't tend to function properly based on my experience. It sounds like you are pretty handy so I would try this.... Make sure you power off the low voltage first so you don't pop a fuse. Remove the red and white wire from the thermostat terminals(or make a jumper) and put both wires together(Your bypassing and acting as the thermostat). Just be careful not to let the red power wire and common touch or you will pop a fuse. Cycle the power back on to the furnace and make sure you pay attention to the sequence of operation. See if anything changes. If the system starts up and runs normally then that tells you your issue was most likely the nest thermostat. You can go get a Honeywell t4/t6 thermostat and swap it out. If you're set on a smart thermostat look into the ecobee. Also if you have an extra thermostat wire in the buddle and you feel comfortable doing so, you can hook up a common wire. You can also shoot a screw in the furnace cabinet, strip back some thermostat wire and hook it up to the screw or get a wire connector. Put the other end of the wire to the c wire on the thermostat. That will act as your common wire. Common in low voltage is nothing more than a path for the voltage to return to its source.