There could also be a fault with the inverter circuit or the CCFLs themselves.
I was just fixing a Samsung P2470HD monitor with a similar problem. I had changed all electrolytic caps - nothing. Then I checked the inverter transformer - it tested as defective.
You can test your inverter transformer as well. Unplug all of the wires from the PSU, then measure the resistance of secondary windings. In my case they were ~1k and ~1.5k. All of them should be of the same value. If there are any other components than CCFLs connected to the secondaries, you can unsolder the transformer and check it again out of circuit to be sure.
Another thing to try would be CCFLs themselves. If you have another working LCD monitor, you can try to hook them up to the inverter of a working monitor. If they light up - the problem is more likely to be in the inverter circuitry.
You may also test the inverter of a non-working monitor with known-good CCFL lamps from another monitor. If they light up - the problem is likely the CCFL lamps or loose connections to them on the defective monitor.
If CCFLs seem to be at fault, you could also check wire connections at the CCFL ends as well. They could come loose and have a bad contact. Listen closely at the corners of your monitor.
If you hear any buzzing or smell any ozone while it's trying to startup, you may have to disassemble the LCD panel and re-solder the wires to CCFLs. In such case this video might help you:
As you may know, there is high voltage (kilovolts) present at the CCFL terminals when the monitor is working, so have in mind not to accidentally touch them if you wish to power your disassembled monitor.
