Furnace has lost it's mind.

[Junkmanstan]

About 4:00am this morning I awoke to an usual sound. I got up and found the furnace running, even though the electronic thermostat was set on A/C. I turned the thermostat off but the furnace continued to run, so I went outside and closed the valve on the propane. After a few minutes the furnace cooled down and shut off. Then, about 20 minutes later the furnace fan came on, even with out propane, so I pulled the furnace fuse on the fuse panel. The thermostat continues to operate the A/C normally. Only thing I can figure out is a fried circuit board – sound about right?

[enblethen]

Could be a bad thermostat.
Disconnect a thermosat wire in the furnace and see what happens. Re-install fuse. If the furnace runs with the wire disconnected, the problem is in furnace. (time delay relay).
If furnace does not operate then thermostat is bad.

[Old-Biscuit]

Sounds like a fried timed delay relay.....either a stay alone separate one OR the one on circuit board.
12V DC power is ON to one side of timed delay relay. When T-stat makes up power is sent to other side of relay heating a coil and allowing power to blower-sail switch, high limit switch and then to board and then to gas valve.

If timed delay relay shorted close furnace would run as normal...but not shut off without pulling power.

Now the question....does your furnace have a separate relay (cheaper to replace) or is it part of circuit board.