When you google for this, you'll find an abundance of theories and information about the cause. This is partly a good thing because it means that it usually varies from case to case so with luck it just might be something you can repair.
This was the second time I had to deal with something like this and indeed the first time It had to do with a defective TFT panel. A quick test to do when it comes to this type of failure is to turn the monitor on, time how long it takes for the problem to show itself, then switch it off, and repeat. Do this about 5 times.
If the time needed appears to shorten with every try: Power it off, wait 30 minutes, and try again. If indeed the problem is taking longer to manifest, and again, that time seems to shorten with every try, then you're possibly dealing with an overheating component that is cooling down when the monitor isn't used for a while, but retaining enough heat between the consequtive tries for problems to manifest sooner.
This was the case with my first monitor. As opposed to the second one I started this entry off with - which never really showed a clear picture - this one would start up like there was no problem, then after a while (about 5 minutes at first) switched to a completely white screen. This monitor also had a bad row in it's TFT panel. With exhaustive detective work (It burned my finger) I managed to track down the heat issue to this:
This was likely also the cause of the dead row in the panel. Obviously not something that can be replaced so this TFT panel was garbage.
But back to the Benq. I did the above mentioned test. Got a consistent error pattern, with no variation in time. The problem would always appear instantly after power on, so I took it apart.
I measured the voltage that the panel was getting. It was 4.5V instead of 5V. Now I didn't really know how sensitive TFT panels are to supply voltage, but this made me glance over to the PSU board and that's when I noticed 6 bulging caps.
(photo shamelessly stolen, as I didn't make any)
All off the dead caps were made by the same manufacturer and there was one more from them that wasn't (yet) bulging. I replaced all of them just to be on the safe side.
The replacements were new Sanyos that were left over from the laptop sla psu project and a couple of pulls from a CRT's PSU board.
And this is why I am now sitting in front of a great 19" TFT monitor (non-widescreen).
I have yet to find any dead pixels, but chances are I wouldn't mind if there were any.
As an added bonus I know that it contains an AU Optronics panel, which is not half bad compared to possible alternatives in the panel lottery :)
That said I wouldn't advise anyone to go out and get a WSOD monitor for repairs. I burned myself with the first one, both literally and figuratively. The only reason I even considered this second one was because I was getting it for peanuts, and from a trusted source. Even if it was beyond repair, I could've still sold it for parts and made more than what I bought it for.