it depends on the failure mode, might be a $2 fix if you have any soldering skills. When you say 'not powering up' you mean to say the power on LED doesn't even light? Or the on LED lights up but you don't see any backlight?
If the LED does come on but you don't see any backlight, try taking a flashlight and shining it directly at the screen when you know something should be there, ie computer on and monitor plugged in. It's possible the backlight failed but the monitor is fine. When you shine the light at a working monitor with a failed backlight you should faintly see what the monitor is displaying from the reflected light.
If the LED doesn't even come on it is probably a power supply problem and hopefully a capacitor problem. Even if the LED does come on but nothing shows up on screen it can still be a PSU problem. I just finished fixing 3 monitors with this problem, all free from work

. What you'll need to do, if you're willing, is open up the monitor and dig into it until you can have a look at the PSU. If you see any capacitors that are bulging out the top or leaking stuff then you have bad caps. Make note of the cap specs printed on the side, go to your local electronics surplus shop, buy replacement caps (usually $0.50each or less) and replace the parts.
Usually there's a section on the PSU PCB with a number of caps clustered together. I just changed out all the caps in that section with new ones even if they weren't bulging. After doing that on my dead monitors, they all powered up fine.
Depending on your monitor, it can be a pain (literally) to open then. Only one of the monitors I had used screws to hold the bezel on, the other two, you have to push the front half of the bezel up to unlatch the plastic clips holding the front and back together. The manual I looked at said to start at the top of the monitor. If you're looking down at the monitor from the top you should see a seam where the two halves of the plastic casing come together. What you want to do is place the tips of your fingers on the inside edge of the bezel (the part that frames the screen) and your thumbs on the back side of the seam. Now you just push up on the bezel, so if you're still looking down from the top, you want the front half to come up towards you. I had to apply a lot of pressure to get it to start to separate. I did this about a month ago and my fingers are still recovering.