The next thing to do is trash it because this thing will kill you. There are some things that are just to dangerous to try to fix. These things kill experienced repair people. I wouldn't even attempt to fix my own and I fix almost anything. Buy a new one or take out a lot of life insurance before working on it.
Does it show anything on the display but won't start? If there's nothing on the display, checking that there's continuity (unplugged of course) on everything that's obviously between the end of the power cord and fuse would be about as far as I could recommend.
If the display is working, I would look to the interlock switch for the door. There is always an interlock on the door of microwaves that prevents them from operating if the door is open, see if you can access this, and test continuity on it and the wiring that leads to it.
I know you obviously have a multimeter, but for other users, to test continuity, you would use a Digital Multimeter to test fuses, wires, and switches.
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