MBP screen randomly going blank/splitting and/or computer freezing

Starting a couple of days ago my MBP (15" late 2011 model) started having problems. The screen now will randomly go completely dark, even though the backlight and keyboard will remain lit. When this happens the keyboard also becomes unresponsive (caps lock won't turn on/off, no key combos do anything). The only thing I can do is turn it off by holding down the power key and turning it on again.

In addition, today when I was working, the screen suddenly split in two, i.e. half of the screen was showing the right side of the content on the left and vice versa with a split in between.

I've tried reinstalling the OS from scratch and it's still happening, so I assume it must be a hardware issue of some sort. I tried running the Apple Hardware Test by starting up and holding the D key but it doesn't seem to work. Any ideas?