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The transformer can certainly cause your unit not to power up. The thermostat and magnetron are for heating so they would not cause for power not to come on. If you are experiencing no power then its either the transformer or the board. Check to see if the transformer is getting resistance. Do you happen to smell burnt wires at all. Typically when a transformer goes out there is an electrical smell. Also try checking to make sure the unit is getting power that its plugged into.
I am sorry something has come up I have to run I will opt out to see if anyone else can help you in the event nobody has picked your question up when I get back I will shoot you the information you are looking for.