Here's what I would try.

Code:

cd /etc/X11
mv xorg.conf xorg.conf.bak
aticonfig --adapter=1,0 --initial
That makes sense, but it results in X failing to load at startup. I had actually already tried something very similar.

I had a look at the BIOS and I couldn't find any option relating to the graphic card.

It seems that I am only able to use the 4200 GPU, it is listed as the default adapter and it bears all the load:

Code:
amdconfig --lsa
* 0. 01:05.0 ATI Mobility Radeon HD 4200 Series
  1. 02:00.0 AMD Radeon HD 6300M Series

* - Default adapter
Code:
aticonfig --odgc --adapter=all

Adapter 0 - ATI Mobility Radeon HD 4200 Series
                            Core (MHz)    Memory (MHz)
           Current Clocks :    203           400
             Current Peak :    500           400
  Configurable Peak Range : [200-500]     [400-400]
                 GPU load :    18%

Adapter 1 - AMD Radeon HD 6300M Series
                            Core (MHz)    Memory (MHz)
           Current Clocks :    750           800
             Current Peak :    750           800
  Configurable Peak Range : [400-750]     [500-800]
                 GPU load :    0%
I couldn't find a command to change the default adapter. Any other ideas?

Thanks for all the help