Radio- you say if you reset it, you get one cycle? Does shutting off
the thermostat (not turning it down but rather turning it off) do the
same thing? If so it sounds like you need a control board.
Without knowing your furnace make and model # I'm purely guessing
you need the Dinosaur board called the Fan 50 plus pins.
You can get one from AmericanRVcompany.com
They had the best price I found after much searching. About $95 including
shipping. (Their Ebay price might be more or less than their own
website price. You should check both if you're interested.)
See my long ordeal trying to get mine working without a new board here--
Suburban Furnace NT20S intermittent operation
I should have taken the advice early on and just got a new board.
That's what I have now and it works fine.
Very easy install. Replaces the old board perfectly- it's literally "plug and