Tony,

If you haven't soldered before and have little DIY experience, it's not
easy to advise you to pursue technical solutions. Here's something easy you
can do. Buy a can of electrical contact cleaner (Radio Shack, most hardware
stores). Turn off the power to the furnace. Disconnect the offending plug.
Spray the connector at the pc board and spray the plug connections. Now plug
and unplug a bunch of times with some wiggling action. If you are lucky you
will remove the corrosion that is causing yur problem. Now plug the plug in
firmly. Restore power and hope for the best.
If that doesn't work I'd recommend finding an honest competent repair
guy.

Dave M.