It is almost 100% certain you either have a failed inverter board or bad back light. If it is the back light, there isn't much you can do to economically repair it. But if it is the inverter board, you might be able to fix it. You can disassemble the monitor and look for the inverter board. Do a Google image search to get an idea of what it should look like.
The easiest repair will be if it has some failed capacitors. Look for bulging or leaking capacitors on it. They'll be pretty obvious. If you are handy with a soldering iron, they are easy to replace. Otherwise, you might be able to buy a replacement inverter board for a reasonable price. Or just replace the monitor.
--Russel