You can ohm out the magnetron with a meter, check across the 2 terminals, should get a reading on your ohm meter, then check each terminal to the metal body, should get no reading. If it passes both those tests it still could be bad, if it fails either of those tests its definitely bad. There are still other items making up the microwave circuit here though, High Voltage Transformer, can be tested with your meter to see if its open or shorted just like you test mag. Could be a bad capacitor, important thing to keep in mind when working on a microwave is the dangers associated just because of this capacitor, even unplugged from the wall the capacitor will hold a very strong charge like a battery. Until you short the cap out to ground working around in there would be like playing with a loaded gun you think is unloaded. You also have a high voltage rectifier diode inside there thats a vital part of this circuit as well. You can test it to see if its good, but most basic meters will not be able to read it due to its high internal resistance, you should get a reading across it one way, then reverse your probes and get no reading.
A power surge like you indicate, and the problems with the display sound more like its a control problem than something in the actual microwave portion. You can test to the side of the HV transformer that power comes in on to see if the control is sending power, you don't want to put your meter on the output side of the HV transformer though to test it for output power, that would be bad for you and your meter the High Voltage output side will be the terminals/wires leading to the mag circuitry, one side usually going to the magnetron, the other side going to the capacitor, again, don't put your meter on this side of the transformer.
There's also likely a fuse, cartridge type and even some thermal disc type TOL type self resetting fuses in there that could be the problem. These usually break the circuit feeding power to the transformer, so if no power to the transformer, follow the wires back to test these. With a wire off to one side of it you should get a 0 ohms reading across them.
Not a lot of techs out there who actually really know how to work on microwaves even if they try to BS their way into thinking they can, sounds like you ran into one of these. Microwaves in reality are rather simple devices though, just watch out for the capacitor in there till you short it out to discharge it. I usually just short a screw driver across its terminals a couple times, then to be sure short the screw driver from the capacitor terminals to ground (metal chassis) with the thing unplugged from the wall of course. It may spark and startle you, usually doesn't, mostly uneventful, but still don;t let it scare you if it does. | 
