I'd say it sounds to me like the backlight inverter is on it's way out.
turn it on and after it blips off...wait a bit until the game boots and shine a bright light into the panel...you should be able to very faintly see the graphics. this means the panel is going...but the backlight is off. if you see nothing you have a decoder board problem. (likely capacitors)
quite often when they start to go, they will take a few tries to get up and running...then often stay running. other times, they will blip up for a second and then shut off.
I've literally swapped out 30 or 40 of these now. it's like their lifetime is up right now.
pull out the old inverter and it should have a number on it you can enter (like DP-04-17019) to ebay and find a new one. (sorry I don't have an exact listing.) I normally just swap them out for a bigger beefy universal type inverter...but the aurora cabinet where the monitor sits is SUPER tight, so you'll need to find an exact sizable replacement or you'll have issues closing the monitor cabinet halves.
they can be had for about 20 bucks.
alternatively you can swap the CCFL tubes for LED. it's a bit of a bear to do, but the results are pretty good. I buy these kits for under 20 as well. I normally only do an LED conversion if the CCFL has broken or is damaged by a failed inverter. the buck driver is super small so it goes anywhere.http://www.ebay.ca/itm/425mm-LED-Backlight-Strip-Kit-Update-19-19-inch-Wide-CCFL-LCD-Screen-to-LED-/281750790742?hash=item4199a7e256:g:yiwAAOSwMmBVp3UX
if you go this route, use caution. you can damage the panel as the glass is VERY thin (about 1mm).