Macbook Pro strange display issues

Last week my Macbook Pro from 2012 suddenly had a display issue. I was working on something using my external monitor (through thunderbolt -> displayPort) when the screen showed some banding and the computer suddenly turned itself off..

Here is a description of what it is currently doing when I turn it back on:

• shows the normal apple start screen with progress bar
• progress bar slowly moves across and then I get some strange banding in the top (see screenshot)
• eventually the progress bar gets stuck about 75-80% of the way and the screen goes to just gray
• and then it switches to being black

Now the screen stays lit up but I don't have a cursor or any way to control it.

I have tried to connect it to various monitors in this state (display port, DVI, etc) all through the thunderbolt display but nothing registers…

Here is a list of what I have tried so far:

• resetting PRAM – keyboard combo works, PRAM resets as it boots again
  but no change
• resetting SMC – keyboard combo works, computer resets
  but no change
• target disk mode – this works, i have it in target disk
  mode now and am backing up files onto my macbook air. I also read a
  post about deleting the com.apple.loginWindow.plist preferences which
  I did but no change

Oddly I found that a lot of 'normal' startup key combinations are not working anymore, even though this used to when i had other issues on this.

Does not work:

• holding down SHIFT to go into safe mode: does not work / no
  difference in startup
• holding down D for diagnostics or V for verbose: does not work
• holding down Control-R for recovery mode: does
  not work

I am making an appointment to at the apple store today after I finish the backup but I am wondering if anybody has any advice. Isn't it odd that these startup options don't work? Also the display lights up and displays the thunderbolt icon fine when it is in target disk mode so that seems like the display is working…

Thank you!
– J