First thing you need to do is have someone call for heat while you are at the furnace, listening and watching with paper and pencil. Write down the sequence of what happens with approximate times. This information is very important for any repair person and will save time and money.
Can you describe where you hear the click? Usually the order of events is the thermostat calls for heat, the inducer starts and runs for maybe 10 to 20 seconds. Once the pressure safety switch in the inducer assembly closes then the ignition for the main burners should attempt to light the main burners. You may have a Hot Surface Ignitor (HSI) that glows red hot or you may have a smaller pilot light that ignites from a spark ignition and then that pilot light ignites the main burners.
If the inducer runs and you see no attempt at any ignition from either the HSI or spark/pilot, then the pressure safety in the inducer assembly is the problem and indicated the inducer fan is not getting the pressures correct. Check that the flue pipe is clean from the furnace to the outside. Check all small hoses for possible breaks.
If you see the HSI glow or spark/pilot light ignite, then you know the inducer is okay and you need to see if the main gas valve opens. You will hear the click of the gas valve and hear the flow of gas to the main burners.
Depending on the primary ignition -
If you have an HSI and it glows and the gas valve opens but there is no ignition. then I would suspect the HSI. It needs to glow red to white hot.
If you have a spark/pilot and the spark lights the pilot flame and then the flame goes out, I would suspect the flame sensor in that assembly.
The more you tell us what happens, the better our answers.
Problems related to residential installations.