If the backlight is shot then it really isnt worth repairing.
Not necessarily. If the monitor is old and too small, then it may not be worth it. Otherwise, the repair may be much less than a new monitor.
Note this could be the inverter and not the bulb itself. In my experience, more inverters go than bulbs. And they are typically easier to replace - though more expensive. Still, if willing to do your own work, and if the monitor (when working) meets your needs, then it is definitely worth repairing.
And even if you do not feel comfortable yourself, an experienced technician can replace both the bulb and inverter in about 1 hour, 2 hours top. So depending on your monitor, and if you expect it to meet your needs for the next couple years, even with 2 hours labor charges, it may be worth the costs of repair.
is a good source. Also if you Google around, you will find sites that specialize in replacing inverters and bulbs - typically at very reasonable costs. But, you have to factor in shipping, and of course, it means your monitor will be bouncing around the back of a truck, twice.