I seem to have fixed my MacBook Pro yesterday, using a small iroda solderpro 50K. It's butane powered and by changing the tip you can make it into a small blowtorch.
Ran the flame just above the chip, moving it around for about 5 minutes. I put a bit of solder on top of the chip to give me an idea of how much heat I was applying. There are little pins protruding through the back of the green, larger part of the chip and I concentrated on those one by one, thinking that they should conduct the heat down to the solder and reflow it.
I was amazed when it worked. I'd been quoted over £300 by a repair company. It may break again but that could happen if I'd have gone with the repair company. Rather I was going to buy a new Mac, so I feel like I've saved myself £1,500.
I've installed smcFanControl to monitor how hot the computer is running. I ran this computer for a long time with poorly lubricated fans. It used to run burning hot so that may have been the reason that it went down originally, but I'm not sure.