Thought I'd share my find after countless forums and message boards with the same problem only to have apple genius tell all the same thing - that it's a logic board issue and that the graphics chip or processor is possibly damaged.
Well I found through other such cases that the logic board doesn't necessarily have to be replaced as the apple geniuses would have us all believing. Apparently pc users get the same problem too, and according to the tech that fix pc's all the time, this screen problem and inability to boot is an easy and fast fix, it's generally related to a graphics chip problem where the solder that binds the chip to the logic board has softened due to overheating. If you take your MBP to a pc tech who also deals in fixing Macs, he will be able to do what's called a reflow or reballing, which is a process of rebinding or resodering any loose pins back to the logic board. According to them this is a simple fix. Only takes two hours max to complete provided your GPU is not fried from the overheating, in which case, yes, you will need a new GPU. Mine was an AMD. I was lucky, it was still good. Only needed the reflow.
So Do as I did, find yourselves a Computer tech in your neighborhood using yelp, mine quoted me only $80USD, and only need to pay if he's able to fix it and if thats the only issue! Of course, for some people, your chip may be cracked or fried, therefore only a new board would be advised, but please try this first before letting apple genius convince you to turn yours in for some ridiculous fees and dollar amounts from $300 and of up to $1200 in some cases I've read on here.
The logic board is repairable folks if it's only loose solder...just as long as there's nothing else wrong with the graphics chip and nothing else is cracked or damaged like the board itself, connectors, the drive, etc...there may be hope yet! So find yourself a pc tech who knows about doing a reflow...this may solve your problem and very cheap money-wise!
...Please pass around!
Cheers!