A furnace that fails to turn on completely can make you think the worst -- that the only option is to replace the appliance. Fortunately, many of the problems that lead to a non-working furnace don't necessarily indicate a complete failure of the furnace itself. Often, only a small repair is needed to get your furnace back in optimum working order again.
Tripped Safety Switch
Many furnaces have a safety mechanism that prevents the furnace from cycling on in the event that the access panel isn't in place. If your furnace stops working after a service visit or filter replacement, verify that the access panel door is properly in place and closed completely.
There are a couple of ways the thermostat can affect the function of the furnace. The simplest is ensuring that thermostat is set to both the "heat" and "fan on" settings; otherwise, your furnace may not power on. If the settings are correct, then thermostat needs to be inspected to verify that it is working properly and receiving power. A failed thermostat needs replaced, whereas a power issue may require rewiring.
Most furnaces are on their own circuit, so if the circuit is tripped then only the furnace will stop working. You can fix this by simply going to the breaker box and finding the switch for the furnace. Turn it completely off, wait a moment, and then flip the breaker back on. If the circuit continues to switch off, you need to have the breaker box inspected by a repair tech to make sure there isn't a short in the wiring, circuit, or furnace.
Gas furnaces typically have a pilot light and ignition system. If any part of this system fails, the furnace won't come on. Problems can range from a faulty or dirty gas valve to a failed ignition system that needs a replacement. The good news is that a malfunctioning pilot or ignition system is typically easily repaired.
The furnace motor runs the blower fan. If the motor fails, the fan won't run and your furnace won't be able to operate. In some cases, the motor may only need a tuneup -- which mainly consists of cleaning and lubricating it. In the event the motor has failed completely, replacement of the motor is necessary.
If your furnace is failing to turn on, call a furnace repair contractor in your area for an inspection and repair.