[UbuntuGnome] Unable to use a discrete GPU on a laptop, vgargb: this pci device is not a vga device

I've installed Ubuntu Gnome 16.04 beta on a brand new laptop because I couldn't get 15.10 live cd to boot on it no matter what I did.
16.04 booted (with nomodeset) and installed just fine. It also asked me to disable Secure Boot, so that proprietary drivers could run, which I did.

My previous (and now dead) laptop used Nvidia's Optimus, too, so I know how to handle most of the problems that come with it. However, the problem I'm getting with 16.04 is completely different and I'm not even sure if this is the right forum to ask for help.

Whenever I boot Ubuntu Gnome, I get a black screen. I read through all the logs and it seems that this time the problem is not with the x server, but with the proprietary driver or maybe even the keel. Here's a screenshot of the keel log:
https://drive.google.com/file/d/0B9G...ew?usp=sharing
It seems that nvidia-modeset allocates and immediately frees the GPU, which is then followed by "vgargb: this pci device is not a vga device" message.

My laptop is Lenovo Z70 with Nvidia 840M discrete GPU. If I purge all the Nvidia stuff (drivers, cuda, prime), it boots to desktop just fine using Intel drivers.
Problem is, I ABSOLUTELY NEED a Linux system with cuda and recent OpenGL (4.3+) support to work on my master's thesis.
I don't care about the Intel card at all. I just want to set the discrete one as the default using nvidia-prime (just like in my old laptop) and forget about it.

I also checked if it's possible to tu off the Intel card altogether from BIOS and the answer is no - I can only disable the discrete one.
Finally, the Nvidia GPU itself is fine. The laptop came with Windows 10 and it works there without any problems.

Any help would be appreciated.