MacBook Pro refuses to boot/recover, hangs at “white screen”

I am somewhat new to caring for Macs, but one has been left in my care and I have not been able to restore it to working order yet. Here are the symptoms:

1. The MacBook Pro would hang with a "white screen" during the boot process. A bit of boot splash would show up, but the gray background would at some point just hang.

2. Booting recovery mode did not work, as far as I remember.

3. Boot from a Ubuntu 14.04.2 USB stick works, provided one attaches "nofb nomodeset" to the kernel commandline (though I put that one down to insufficient driver support). I have no idea whether or not these usually work out-of-the-box.

4. Using parted from the aforementioned stick, I was able to see three partitions, one EFI Boot, one large main partition and one labeled Recovery. It seemed strange that the recovery was recoognized as HFS+, as I expected, but the "main" partition was not mountable and did not show a filesystem type.

5. I also discovered that the drive in question was an OCZ Vertex3 256 GB, which I assume is not standard? The previous owner could have upgraded it.

6. At this point, I decided to wipe the drive and try with a fresh installation. I removed the SSD from the MacBook, pulled a full disk image from my desktop just in case (which went without any read errors) and used hdparm to do an SATA enhanced erase, leaving me with a "fresh" disk. Then I put it back in.

7. I started internet recovery, which loaded, showing me the global and everything. Afterwards, it rebooted, showing me the Apple Logo. But then I run into the original "white screen" again.

8. I've tried resetting the NVRAM on boot, which succeeded because it turned the boot chime back on, but even then, running internet recovery again just causes it to hang on the white screen.

9. There seems to be either very high CPU or GPU usage on the white screen, as the fans start wailing pretty intensely, also the body gets very hot in a very short time.

10. For funsies, I installed Ubuntu onto the MacBook, which works (after smoothing over a few hiccups, fortunately I have lot more experience doing that).

11. Recovery mode (Cmd+R) and Apple Hardware Test (D?) I have not been able to run. The former suffers the same white screen issue as described above.

Currently, my only vague guess is a GPU issue, that may be circumvented by Ubuntu by using the not completely feature complete open source radeon drivers. But that is a wild guess. Any input is appreciated.