Have a look here Backlight repair guidehttp://www.dnd.utwente.nl/~grit/backlight/ccft.html.
The only way to check the lamps, CCFLs (Cold Cathode Flourescent Lamps) is by substitution, they are about as thick as a knitting needle and if not thinner, the length obviously depends on the screen size... BE WARNED they are very fragile.
LCD monitor or TV displays can be treated as the same, some are easy to replace some are a 'pain'... again some are a 'U' tube shape, more often than not it requires complete dis-assembly of the screen because they are sometimes held in with tiny nylon clips to avoid vibration and breakage.
They are kinda like a flourescent tubes you see in overhead lighting but without the filament heaters at both ends, the inverter generates about 1.8KV or 1,800V off load and generates about 1,400V when the tubes are lit.
Tubes don't normally just 'go' (unless they have been cracked), normally the whites in the display become tinted or discoloured, the picture 'may' become dimmer in the process, then the next stage of their demise is a flicker.
Of course inverters can give this kind of symptom and they can also just go and refuse to work.
Don't be tempted to measure the voltage from the inverter you need a proper high voltage device, the normal type of test meter will not do unless you have a special high voltage adapter, again the only way is by substitution.