I had a similar problem a few years ago. Fan would blow--no heat.
Someone suggested that the initial startup to clear the area of Carbon Monoxide was supposed to trip a switch--Might be called a sail switch. If that switch was stuck or the battery did not provide enough juice to clear the air, the switch would not trip and the igniter would not light, but, the fan would start up. That might explain why the fan kept blowing since the circuitry is designed to run after the furnace is shut down. That's exactly what happened to me.
I had been dry camping and the battery was not fully charged since my class C wasn't moved for a few days. Furnace mysteriously started working again later, after I had driven.