My furnace Lennox G20Q3/4E-100-5 behaves as follows:
1) Fan is on "Auto"
2) Thermostat calls for heat
3) Flame occurs
4) Blower doesn't come "On". After a while, the burner stops due to safety. It retries again, and same thing happens.
5) When the burner is "On", I put the blower on "Fan On" mode and the furnace keeps running until it meets the thermostat set-point. Then the burner goes "Off".
Blower keeps running, because it's on "Fan On" forced mode.

I see where someone had same problem just need to know where can I purchase the controller board or even the relays for the board would be even better.

My location Toronto Canada.

You have a fan control problem in the auto mode.

Here is your service manual. Looks like it is a board problem.

http://0190acd.netsolhost.com/manuals/G20_Series.pdf

I figured it was the controller board I'm trying to find similar boards (defective) that I could scavenge some parts such as a relay to see if that resolve the issue. The furnace did this once before but started working again after I had set the thermostat to a much higher temperature.