MINTEMP will trigger if the heater doesn't heat up within a certain period of time or possibly show that its heating when it should be.
Does the thermistor seem to work? grab the cold heater block with your hand and see if the temp goes up a few degrees
If it's fine, check the resistance of the heater (with all power off). Since its a 30W heater, i'd expect the resistance to be about 19-20 ohms. If that seems fine, then check that there is voltage across the hotend heater terminals on the control board when it should be heating (with your DC voltmeter: it should be 0 before heat is on, and 24V as soon as it is turned on).
it's either a thermistor, heater, wiring, control board, (or possibly firmware, but since you are probably using stock, I doubt that's it)... but certainly fixable