I see this question is backdated a bit and hasn't been replied to. I dont know if you still need input on this one or if its too late.
LED one indicates that the logic board is receiving a trickle charge from the PSU. when you push the power button, the second LED should come on, indicating that full power has been received, then the 3rd indicates the GPU initialising, and the 4th indicates the LCD is connected and enabled.
if you get no second LED, then i'd initially check that the power button hasn't been damaged.
You can start by unplugging it and shorting out the power pins.
If you still get no response, then it could be PSU or logic board, but its hard to trace without a process of elimination of some kind.
I hope this helps.