Tie the two blue wires together. This should start the furnace fan, in 10-15 seconds the burner should come on. If this happens let it run for a few minutes. Now separate the two wires, the furnace burner should stop, furnace go into cool down mode then shut off.
If this all happens, you have a bad thermostat or the thermostat switch is in the wrong position.
Post make and model of thermostat.
If the fan starts but the burner does not start, the sil switch is not making contact. Could be a speck of dust. Use compressed air to blow out sail switch. Located in the back upper area of air fan housing.