I know this thread is a couple of years old but thought I'd post up my repair experience regarding this monitor in hopes that it can help someone along in the future.
My w1907 had an issue similar to this one. It would power on and the screen would stay black, but the indicator LED in the power switch would go blue, then flash orange and go back to blue every 5 or so seconds...almost like it was trying to come out of sleep mode. If you left it on long enough, eventually the screen might come up and work fine but not every time.
On a hunch I figured I couldn't possibly make it any worse, so thought I'd try my hand at making a repair attempt.
I have been an electronics tech/engineer for a little over 20 years, have designed and built countless guitar amplifiers and various other electronic guitar gear over the years. But of all the things I've ever repaired a computer monitor is not one of them until now.
Following some simple disassembly instructions online, I carefully removed the black trim ring with a flat tipped screw driver between the side of the ring and the rest of the display housing. Once that was out, I disconnected the power switch PCB, lifted the screen assembly out of the housing and disconnected the button PCB. Once the assembly was out, I disconnected the 4 display connectors and the 2 speaker connectors, unscrewed the 4 hex nuts from the SVGA/DVI D-connectors and the 2 phillips screws from the IEC receptacle, then unscrewed the 4 screws on the display itself (there are two on each end of the display). Upon lifting the inverter assembly from the display, I reached in and disconnected the display's ribbon cable from the display driver PCB, then set it aside sitting on a soft piece of cloth where it would not get damaged. Once that was out of the way, I then proceeded to remove the inverter PCB.
On that board are several electrolytic capacitors. One of them, component ID C818, had a bulged top like it was getting ready to leak. I unsoldered this capacitor and checked it with my Fluke 189, and it measured about 50% of its marked value and was slowly decreasing in measured value on the meter.
Took a trip to Radio Shack and bought a 1000uF/35V radial electrolytic capacitor. The original one was a 1000uF/10V so the replacement capacitor I used had a better voltage rating. Replaced the cap, reassembled the display, hooked it all up and turned it on.
Low and behold the display fired right up and the display came on right away!
So check all of the electrolytic capacitors on the inverter board. They look like little batteries on the inverter PCB. The tops of them should be nice and flat. If any of them appear to have a bulge in the top, replace them with capacitors of identical capacitance rating and a voltage rating that is equal to or greater than the stock units (I think most of them are underrated in voltage spec for the duty they're seeing to be honest. Never hurts to use capacitors of a greater voltage rating).
This fix may or may not fully rectify your display issue, but I can say that if you find any capacitors with bulging and/or leaking tops, they are fried and should be replaced anyway. It just so happened to rectify the issue that I was having and perhaps it could work for you as well. At the very least, replacing any bulged and/or leaking capacitors will rule them out as the cause of the issue.