@Bokefas: Can you go into your BIOS and see if there is a Graphics Option for "Primary Adapter" or "Primary Display Adapter"? If so, set it to the Intel Graphics, save settings, reboot - and let me know if there is still a black screen.
@Ormaslash: A 3rd party graphics card is a separate component of a system. Our graphics are built into the processor itself, some laptop OEM's will include a second "Discrete Card" (aka 3rd party card). According to your OEM's website, your system supposedly includes one of these. However, you need to contact the OEM of your system to verify that. When you inquire with them about this, if they confirm that there is in fact a discrete card inside - confirm whether or not the system is supposed to be a switchable graphics system, or 3rd party card only.
@rikirk: Please attach those screenshots as well 
@rtdroid72: They must be listening to us, as now there is an Intel® driver showing up. However, its one of the old drivers (3071 from April this year!). I won't suggest downgrading your driver to it just yet. Can you check your BIOS and see if there is a Primary Adapter option? If so, make sure it is set to the Intel option. Let me know if you even have this option or not too!
@Tarlach: Can you verify a few things for me please? Firstly, in the BIOS there may be a section for "max graphics virtual memory" or something similar. Can you verify that it is set at the highest value available? Additionally, how much memory is in the system? Also, please attach a copy of the systems DxDiag (Start -> Run -> DxDiag -> Save All Information).
@Billybumper: Can you verify with your OEM whether or not that system has support for Windows* 8.1 yet? Looking at the support site for your product they only provide drivers for Windows* XP and Windows* 7. Likely there will need to be a BIOS update for the system before it will function properly with Windows* 8 or Windows* 8.1.
@FinnGus: Try the following; Go into the Tiles interface, type "Device Installation Settings" and choose the control panel option that shows up. Change the setting to "No, let me choose what to do" and set it to "Never install driver software from Windows Update". Then go back into Tiles and type; "Windows Update", choose the option for "Windows Update Settings". Then go to "Choose how updates get installed" and change it to "Download updates but let me choose whether to install them." Reboot. Do the re-install process again and install 3345. Theoretically you should not have it auto-installing more drivers now. Let me know if you are still getting Code 43/31 after having 3345 installed AND rebooted.
Thanks!
-Nic