i fixed a monitor like that before, but it requires some manual "editing" of the monitor settings... i dont recommend this but it might be a last resort:
it's actually pretty simple all you need is a long thing crosshead (dunno actual word in english) screwdriver
you unscrew the lid of the monitor (usualy it's screwed on with 4-5 screws and slides off the back be sure to remove the powercable and detach it from your computer first)
depending on the monitor type you'll see several white plastic screws (might be different, as i said depends on the monitor type) these change the settings of the monitor (brightness, etc)
it's just a matter of finding the right one and giving it a few turns with the screwdriver. BEWARE! to actually view the changes you'll have to reattach the screen while the lid is off, this means there's a chance you might get an electric shock if you're not carefull, best thing to do is to let someone who knows their way around electricity do it. you'll need to work with 2 anyway, one to keep an eye on the screen to see what happens, i did it alone and it took me half an hour to get the screen right (mainly because i touched the wrong screws without knowing and had to experiment to get the screen back to normal)
again, i dont recommend this, but it's a last resort and it will fix your screen to normal brightness no matter what game or program you run
little sidenote, if you do this and the screen turns dark again after a while, you're monitor is busted, either change it manually every time it turns dark or get it replaced