So far we have replaced the control module, tested and confirmed operation of the transformer, checked voltage to the unit, replaced thermostat and confirmed connection by jumping red and white lines to call for heat, replaced a fuse that was okay, but decided to try it...
We've check the wires, everything is tight. New filter... (sigh)

We can hear the furnace relays clicking when the thermostat sends a call for heat, but that's all we get. The draft motor does not come on, and there's no spark for the pilot light. According to the new control module, the led's lack of any light means there's no call for heat - which we have tested - meaning the call for heat isn't being recognized?

What else can we do? We're freezing, limited on funds, and desperate. Thanks

EDIT: Never mind. Turns out the draft motor is gone. Power is reaching it, but it just gets hot and hums, but doesn't move. (Explanation for anyone with similar problems - check the draft motor. Control Module does not power up until pressure switch is activated - thus no led status light if the draft motor doesn't run to activate the pressure switch.) Guess our new (unnecessary)furnace parts and new thermostat go toward preventing future failures. Worth the money in the long run. Still paid less than having a pro come out.

Good job on the repair, and thanks for posting results, may help someone else. Thanks