Sometimes my microwave trips the other circuit that has our computers
on it, even though the appliance is on a different circuit at the far
end of the house. This happens maybe 1 out of 3 starts.

I've replaced the GFCI and it still trips; moved the microwave to a
third different circuit - same problem.

The microwave has been working normally for almost 5 years, but has
recently started making a buzzing sound on start up.