If the inverter has gone bad, there is rarely a visual sign of the failure. A bad one looks just like a good one to the naked eye.
Replacing the inverter is easy if you have already opened up the plastics around the screen. Plus, it's one of the cheap parts to replace. It's as simple as unplugging the old inverter and plugging a new one in it's place. Always remove the battery, unplug and drain power before (un)plugging anything internally!
If you have a local computer repair shop (not Best Buy - look for a place that only exists locally
) they could have a tester that can tell if the backlight inside the screen is bad.