Furnaces contain a number of parts that can break, but thermostat problems often cause a furnace to fail to fire. If the combustion process fails, a broken pilot light or electrical switch may be to blame.
Digital thermostats sometimes indicate if their connection to the furnace is broken. In some cases, a wire may have disconnected. Electrical components within the thermostat itself may cause the unit not to display anything. Non-digital thermostats are a bit more difficult to check and may require expert inspection.
Furnaces need a source of ignition to start burning gas. Pilot lights were common in the past, and simply relighting the pilot light can get the system up and running again. However, it's important to ensure that the main gas line is not flowing to prevent flashes and burns. Most newer systems use electrical switches, which don't waste gas to run. Replacing the unit can fix this problem.
More complex problems include obstructions of the gas line or a disconnected unit. If the gas line is open and no gas flows, it's important to call a professional. Gas leaks in or near the home can lead to explosions. If the pipe is obstructed, dangerous levels of gas can build up, and expert care is needed to clean or replace the piping safely.