Question: My friend has a circa 2006 A1212 Macbook Pro 17inch. It has issues starting up but when it boots everything works fine but the screen is all pixelated, flashes randomly, and some parts have a red tint. 

I think the video card is dying and that was the general consensus on the internet (note: external monitor has same effects).

Is there a way to salvage this machine or get it in a better working condition without replacing the logic board?

Answer: 
The GPU and CPU are all soldered to the logic board, so in theory someone with enough skill and tools could repair the logic board itself, but in practice replacing the board or the computer is more cost effective in almost all cases.
I had a similar problem with my A1212 Macbook Pro 17inch. This is what worked for me:

<http://www.youtube.com/watch?v=outHBB4AlB4>

And here is instruction how to remove logic board:

<http://www.ifixit.com/Guide/MacBook-Pro-17-Inch-Models-A1151-A1212-A1229-and-A1261-Logic-Board-Replacement/325/1>