I can't get my A/C or furnace to come on. The fuses seem to be OK, my furnace switch is on, and I've even put in a new thermostat. What next?

Have you checked the breakers or fuses, if so next check for low voltage power at the transformer,if it's a gas furnace it should have 120 V going in and 24-27 volts coming out
If its elect. It will have 220 going in,, if its gas make sure the doors are on tight ,It`ll have a switch that kills power when doors are off,, check out and tell us how it goes,, you could even have a bad breaker that looks on but no power traansfer,,