My first inclination is that the thermostat is bad. The kind that tell you when a system is on or off are not reliable in my opinion. If it is ok then there are many reasons why the furnace would not come on. All of the safety switches have to close, signal is sent to the gas valve, the inducer fan should have come on first, gas valve wont open valve unless the ignition system is working.(standing pilot, spark ignition, or hot surface ingnitor). They each have there own checks for proper function. Im sorry i cant be more specific, but the information provided doesnt give me anything else to draw conclusions from. Good luck