First thing to do is measure the output voltages of the power board. You're looking for the one that provides standby power, usually +5V or +3.4 V and in some rare cases other voltages.
Don't know what it is for your TV, but it will sure be available on the power board if you see the red LED there.
Next you look to see if upon pressing power the main board signals to the power board to turn itself fully on, i.e. start generating the rest of the supply voltages.
There's a pin on the power board's connectors that is labelled "PS_ON" or just "ON" or something similar.
It should raise to +3V or so when you press the ON button.
For an example of a simple power board see this:
http://blog.coppelltvrepair.com/2010/09/how-to-test-power-supply-r0804-0901.html
If you do not receive that signal then the problem is in the main board.
if you receive that signal, but the power board does not generate the additional voltages that it outputs to the other boards then the problem is in there.
And if it wakes up and provides those voltages but the TV is still dead then the problem is in the main board, which usually needs to be replaced.
Hope this helps. If it does do not forget to rate it :-)
if you need more help - supposedly paid though - feel free to contact us.
www.coppelltvrepair.com