Thermostats are very reliable controls, and it's rare that anything actually goes wrong with the thermostat itself.
It's far more likely that something else is preventing the heating system from coming on.
Thermostats work on 24 volts AC, whereas the rest of the circuits in your house are 110 volt AC. So, there will be circuit breaker in your house's breaker panel that provides power 110 volt AC power to the heating system and a transformer that converts that 110 volt AC power to 24 volt AC power for the heating system to use. So, the first thing to do is check that the circuit breaker for the heating system isn't tripped, and the next thing to do is check that the transformer for it is producing 24 volts AC at the output terminals.
If you have 24 volts AC at the output terminals of the transformer, then you should be getting 24 volts AC at the gas valve of the boiler or furnace when you turn the thermostat up. If you don't, then the problem MAY be the thermostat itself, but it's more likely to be one of the safety controls in the primary circuit preventing the 24 volt power from getting to the gas valve. If you do get 24 volts AC to the gas valve, and the furnace or boiler isn't firing up, check that there's a pilot light burning.
If the pilot light is out, then check that the main gas shut off valve to your house is open. The way to tell is that there will be some straight line or mark or something on the thing that turns on the gas shut off valve. If that thing is PARALLEL to the valve body, the valve is open. If that thing is PERPENDICULAR to the valve body, then the gas is shut off. You need to turn that thing so that it's parallel to the valve body to turn the gas back on.
If the main gas shut off valve is open, then try lighting the pilot light. If the pilot light burns, but goes out by itself, the most common cause of the pilot light going out is an old thermocouple. If you connect a new thermocouple to the gas valve and have a helper heat it with a butane lighter or candle, then if you can cause the boiler or furnace to come on by turning the thermostat up, then the problem was a bad thermocouple, and it needs to be replaced.