Hello Mike, welcome to justanswer. It is sounding like a cold solder or a loose solder problem. Specially the transformer side. If I am not mistaken, this is a step down transformer for the digital side of the controller so it should be 12 volts secondary. If you can not read 12 volts, it might mean an open primary but not an open secondary since the wires of the secondary are far too big with respect to the primary.
What I can suggest is for you to get a soldering iron, then weld again all the joints that you can see on the transformer terminals. Fill it up as much as you can with new solder and you might get it to work.
If you are looking for a new board, You can order it here, look for the inverter. That is the only pc board that I found. Please click the blue word.
Thank you for your advice. I had already done all of things you suggested. I had gotten prices for the new board, but wanted to see what the secondary voltage was. There are two test points on the board- one says 18Vand the other is 5V. Guess I'll find a 12v transformer and cross my fingers. The microwave is not worth another 85$ Thanks for your generous advice. I would gladly recommend you to any one else with their appliance problems. T/U- Mike