Can I measure the ~500-700 volts of voltage in the invertor of an ordinary LCD monitor with a simple multimeter So I can diagnose it?
You could get a meter which would be used in between the power cable and the power socket. They aren't that expensive you could probably pick one up at the local hardware or electronics store.
You can try to use a high impedance digital multimeter (voltmeter) on the scale 1000 V AC, but the output of the inverter has a high internal resistance, and thus, the voltage will be very different when the load is connected and when it is not (in this case, could be very high, maybe over the end of the scale, but it's not an indication that it's working well). Also, the inverter works at high frequency and usual multimeters (including digital ones) cannot work well at those frequencies: so, it might show something even if it's only one test wire connected (!). The best approach I recommend to you is to test this output by comparing it to a good working monitor, if possible of the same type, with the load connected, and paying attention not to touch with fingers anyone of the test wires. So, if the voltage (on load) in the suspected monitor is lower then 2/3 then the one measured on the good one, you can suspect the inverter.
Most electronics carry a sticker that say--NO Serviceable Parts(inside). There are also UL.labels. .and the standard OUTPUT--of devices. Your question seems a waste of time.over-all.about todays electronics. I also.would NOT use a Voltage Inverter on expensive devices. Unless it was specifically--designed for the particular device. Can you measure the output of a device?.YES.most times you can meansure any electrical device Concerning your specific question.your wasting your time.