Thermostat failing?

[cabmandone]

I'd be curious to know if your furnace has a circuit board with a light to display codes. From what you described when the furnace would light it would burn but the main fan would not energize. If it remained lit long enough it should have tripped the limit switch. It sounds like you found the problem but it would be interesting to know how long the burner was staying on before cutting out and whether there were any active codes.