Take a look at this thread on how to set the jumpers on the motherboard.
You will also have to connect at least one of the cables from the motherboard to the card to get the power there.
The GeForce GTX 980 Ti’s TDP is 250W, according to Nvidia. But it never reaches that number under normal conditions so you should be fine with the 230W PS. Basically the jumpers tell the motherboard that the 230W PS is dedicated to the graphics card whilst the 180W is used for the rest of the computer.
If you need help with opening your PC, check out Welsh Gamers Youtube video's. They helped me a lot.
I have a G20AJ and my 230watt power block (admittedly not an ASUS branded one by the looks of it), only occupies a single power socket, with an extra socket available for the 180watt branded ASUS power supply.
Now the 180watt one I got was :
New Original Asus 19.5v 9.23A 180W ADP-180MB F FA180PM111 AC Adapter Charger , from fleabay, it should be noted that the seller has now doubled the price on the listing !!, but there are plenty of them out there, it's just I wanted mine next day.
Going back to one of the other replies, I would make sure you connect both cables from the motherboard to the gpu if it needs them, I made the mistake of loosely connecting one and spending an afternoon trying to fault find why my system would crash under load, so it appears at least in my case, both are needed.
I hope this helps, if you are still having issues maybe upload a picture to show what PSU you have ATM.
If I am looking at those pictures correctly it looks like you already have both the 230W and 180W power adapters. They look like they are in the proprietary ASUS adapter holder. With that you would also have two cables that plug into power in the wall, correct?
So, all you should need is the new card. It should come with the internal power cable(s). Just plug and go.
I would'nt even look at putting the 980ti into the pc now when the 10series are out and use way less power and much more powerful, the 180watt power brick won't be good enough for the gtx 980ti, you will need a 230watt power brick
GTX 980ti is not 100% compatible with ROG G20, even when you use 330w power brick it`s only draw 230watt max due to limited input power board. I used gtx980 ti with alienware 330w power brick before on G20aj, you need to decrease the power limit of the GPU to 90% (with msi afterburner), if not it wont be 100% stable and it will crash on some apps that using full power of the GPU.