You say that the furnace runs for about 3 minutes. Are you saying that the burners, inducer motor and the fan blower are running for 3 minutes and then the main burners drop out? Three minutes is a pretty fast limit for a furnace with for an operating fan, clean filters and a/c coil, and no ducting restrictions. Do you have an electrical meter to determine where the voltage stops on the safety limit, roll out switches and inducer's pressure switch circuit that shuts down the gas valve. Do you know if the gas valve is still getting 24V when the gas valve shuts down? Can you see a change in the flame around the flame sensor just before it shut's down? Measuring the temp rise of the furnace and comparing it to the temp rise on the furnace plate will tell you if the limit is supposed to be shutting down the burners. Make sure any ground wires are securely connected to bare metal. Is there a flashing diagnostic led on your board that corresponds to a fault legend on the furnace door?