lol, never tried that one before...
That's actually the classic test for backlight or inverter failure. You can't really tell which has failed with this, but it does tell you if the monitor is getting and processing a signal or not. Newer LED LCDs don't use CCFL tubes or inverters, so this test won't work with them.
Parts are typically $50 to $150, depending on size of the screen and availability. Any reputable repair shop can do the job in 1 hour, 2 tops so from there, you can determine labor charges. That said, many shops charge a flat labor rate (plus parts) for replacing inverters and backlights, so call around. And there are some repair shops on-line that specialize in these repairs where you can send the monitor to.
If you are handy at these sort of things, you can fix it yourself - it is not really hard. In fact, figuring out how to open up the monitor's case is often the biggest challenge. There are many good tutorials