RJ45 Loopback Adaptor Method of Power Up
To correctly configure this, build the circuit as above. There is two relays - both turned on when the IGN is live. One relay cuts and supplies power to the AC adaptor (and screen in my case), and the other relay connects pins 2 and 6 (looking at the plug with the gold contacts facing up) of the RJ45 ethernet plug. Pins 1 and 3 must be soldered together permanently. This device is called a Loopback adaptor, and will not cause any damage to your laptop.
You then need to configure Windows to allow Wake On Link (not all network cards support it). Right Click "My Computer" > Select "Properties" > Select "Hardware" > Click "Device Manager" > Right Click Your Network Card > Select "Properties" > Select "Advanced" ...
Then you need to look for options relating to Wake On Link (WOL). On my network card (Intel), I had to Disable Intelligent Power Control and Force Wake On Link. You will need to find any options relating to the card's power usage (if there) and anything to do with it waking.
So the principal is, when pins 1+3 and 2+6 are connected, when the computer is off, it will turn itself on - without you requiring to turn on the laptop with the power button.
Something to bear in mind with this connection is that if you shutdown the computer with the IGN still live, it will not boot up again when pins 1+3 are connected. The computer *MUST* shutdown with all relays turned off.