Here's
more information than you probably wanted to know about microwave oven repair. Please pay particular attention to the safety information here—while it's certainly possible to work with microwave ovens safely, they have lethal electrical voltages when in operation (and potentially even when unplugged if the bleeder resistor is broken—and bear in mind you know something is broken on your oven.)
If it's not a relatively simple problem to fix, it's probably more cost effective to buy a replacement oven these days. (A simple fix would be the main fuse, cleaning the door safety switch mechanism of accumulated crud, perhaps cleaning junk out of the waveguide, etc.) If you want to microwave under inverter power, I'd suggest looking into replacing it with a Panasonic Inverter model; these have some rather significant advantages over traditional designs particularly for inverter operation. (Specifically, they're more efficient; they are less affected by strange AC waveforms such as MSW inverters produce; and their maximum power consumption actually is reduced as cooking power is reduced, rather than merely cycling on and off as virtually all other units do, which reduces the peak loading on the system.)
