The problem you are having is due to the edge connector on the main blower board. What you will need to do is shut the power off to the furnace pull the edge connector off and look inside of it, this is a flat white piece of plastic with about eight wires in it that connects on the edge of the blower board. There will be little finger looking pieces in there. If the finger pieces are corroded completely off you will have to replace the wiring harness. If they are just corroded you can unplug the furnace and dip the edge plug into a glass of Coke, when the corrosion is gone dip it into a glass of water to clean all the Coke off of it. Use canned air that you use on your computer keyboard and blow out well. Reinstall edge plug back on the board and see if it works properly. You cannot use Pepsi or anything with a high sugar content to do this. If you need the wiring harness it is part #311235-401. If you need any further assistance let me know.
I took the liberty of finding a website for you that has the wiring harness. If you follow this link and enter the part #, scroll down you will see the wiring harness. http://americanhvacparts.com/Merchant2/merchant.mvc