PRIME should have been used by default if you boot without nomodeset.
You might try using some other distribution which can actually boot...

Okay, thank you for all your help.

Another option is the generic modesetting driver built into the server since version 1.17.x. It's where the focus of Xorg driver for Intel gfx development has shifted. Easiest way I know to configure that the modesetting driver be used in *buntu is to purge whichever of xserver-xorg-video-radeon, xserver-xorg-video-amdgpu and/or xserver-xorg-video-ati are installed. If the modesetting driver turns out not to help, it's easy enough to boot in rescue mode and reinstall the other(s).

I know this is pretty old, but as far as I can tell, this problem still affects multiple people out there, and no one has found a solution.

As a summary: During boot, the X server crashes, and the computer either shuts down or reboots only to crash again at the same point. This affects only AMD dual GPU setups with a dGPU and iGPU (a very common set up). Boot may be rescued by invoking the nomodeset boot parameter. This disables all GPU(s) functions, and replaces them with software emulation. While this is sufficient to get into the system for recovery and troubleshooting, it is not an acceptable working solution.

No one seems to have mentioned this yet, but a partial workaround is to set radeon.dpm=0 parameter instead of nomodeset. This disables graphics card switching, which means it disables the dGPU. This boots normally, and you get the function of your iGPU. This is an acceptable working solution for very light use (browsing, playing videos < 4k resolution, music). It is however, not acceptable as a final solution. In mose cases iGPUs are very weak, and even things like resizing application windows will cause lag. Enabling the dGPU after boot immediately crashes the X server.

This problem has been around for 6 months now, and occurred around (maybe caused by) the deprecation of UMS (Userspace Mode Setting). There has been zero progress on it. I would appreciate any advice.

P.S. my setup works perfectly on all version of Windows, and used to work on *buntu up to 15.10 perfectly, until the release of 16.04 which caused this problem even in earlier versions of *buntu (among a whole host of other issues).

P.P.S Why is the thread titled "[Solved]"?

radeon.dpm is Dynamic Power Management. You should definitely leave it ON on a laptop.
Also did you try any other distro than Ubuntu?