I installed the Intel Graphics Update software to just give it a go, unfortunately I've had some issues since, and now I am currently to bring back the system to it's previous working state. The issues are:
Unable to input passphrase for LUKS encryption at splash - I need to remove "splash" from the boot options in Grub2.
The system are unable to wake up after suspend. Instead the screen is black and the system seem to be unable to take inputs - meaning that Ctrl+Alt+F* does not work. I have to do a hard reset of the system.
Also Compiz (Unity) is acting odd. Unable to set scale for menus and such, and my workspaces are gone. Both are activated, but does not work.
I have removed the repository, uninstalled the packages and also did this: How to safely remove proprietary Intel driver.
I don't know what more to do, but it still doesn't work to boot with splash, or to suspend the laptop any more.
In system details, graphics now say: Gallium 0.4 on llvmpipe (LLVM 3.8, 256 bits)
lspci -nnk | grep -iA2 vga:
00:02.0 VGA compatible controller [0300]: Intel Corporation Haswell-ULT Integrated Graphics Controller [8086:0a16] (rev 09)
Subsystem: ASUSTeK Computer Inc. Haswell-ULT Integrated Graphics Controller [1043:142d]
Kernel modules: i915
So after doing some further reading and searching I found the package i915-4.6.3-4.4.0-dkms, which I removed (or purged) together with the intel-graphics-update-tool and it's source.list. Now all issues are gone. To think that one package (the first one above) would possess the ability to screw up a system that much. But now I can enter my pass at boot, suspend, and compiz works again.