I found a pair of LCD monitors, both with an identical problem: when turned on, the CCFL backlight lights for about a second, then goes out. The LCD itself remains working, but of course is nearly invisible.
These are plague monitors: the low voltage "samyoung" caps were bulging from both ends. I replaced them, and even replaced the high voltage cap, but it didn't work. The power rails all read steady at their rated voltages, even during the attempted backlight startup. I didn't replace the smaller low voltage electrolytics, but they appear fine.
The CCFL tubes themselves seem fine. I connected a different CCFL to the inverter, which does the same thing.
Any ideas?