These guys have tons of parts at the right price...check them out when you find the part you need for your fix. Hope that helps!
The power supply board could very well be defective. I would also check the Zsus board and the Xsus boards. If either of these boards fail it could also cause the power supply board to fail.
You can unplug the connectors to the zsus board at the power supply and try to turn the set on. If it does turn on, the power supply board is ok. If not, the power supply is bad. If the power supply board is ok, undo the plug connectors that power the Xsus board and hook up the plug connectors to the Zsus board. Turn the set an and see if it stays on or shuts down. Part numbers should be on the boards. Zenith is really LG Corp. Their customer support number is 1800-243-0000.
Hope this helps,