Have an old furnace, at least 18 years old, pilot light is lit and stays on, but the burners do not light, installed new thermostat the other day and it fired up right away, but when I turned the heat off two days later that is when this problem happened, what can be the reason?

If it's a standing pilot furnace you may have a gas valve sticking and not letting gas through to the main burners. Its hard to say with out knowing the make and model of the system.