Might help...my thermostat made good contact and started (conducted elec to furnace) 70% of time and failed to start 30% of time. I cleaned up contacts and now furnace works 100%.
I tried all kinds of stuff (making sure wires were connected all the time, cleaned out combustion chamber, etc)
Somebody on here recommended to clean up contacts. Simple 30 sec job on old style thermostat and it solved the problem.