For testing inverters, rather than measuring the voltage with the gadget powered up, take the inverter out and measure the resistance of the transformer(s), which is the part that fails 90% of the time. The primary, which will be connected to V+ and an FET should measure between half an Ohm and a couple of Ohms. A good high Voltage side will measure 700-1000 Ohms in most cases. If the transformer coil looks partly burnt, it's toast.

Occasionally an FET will short. In this case, the FET and surrounding parts on the PCB will usually look burnt, and it will take the transformer with it.

An identical computer with a cracked LCD is usually a cheap source for a replacement inverter. For desktop monitors with 4 or 6 fluorescent tubes and transformers, only one transformer may be bad, so one donor display can fix several.