Most of the time it's a door switch problem and the door switches are on the neural side of the circuit on most of them. The circuit boards control the line voltage and the safety door switches control the neutral to complete the circuit. You said you have 120 volts at the transformer but did you measure 120 between the terminals or just the presence of 120 to ground. Mag tubes have two different voltages on the same wires. You have a low voltage (3-5) ac volts that heat the mag tube end until it glows and then the high voltage 2000 volts DC that is what makes the RF energy. Older units had separate transformers for both voltages but now they are combined. The tube heat up time is why the unit operates for about 3 seconds unit you hear the power surge as the microwave finally lights off. These mag tubes light up just like the old tubes in antique radios and tv's.