Josiegallo, That is exactly the same scenario as my problem, and I got mine fixed with no issues for free at the apple store. the NVIDA chip is soldered to the board, that's the only reason the logic board needs to be replaced. it's all one unit. it all depends on who you talk to. Unfortunately there are people out there who are trying to "pull a fast one", which then makes people suspicious of us who really deserve to get something fixed for free. I didn't even have to ask to get mine done free, they just offered. So it depends on who you talk to.
But I had the same intermittent issues and finally just light went on, no chimes, etc., just like yours.
I did find some posts that could be interesting to you...something you could try if they won't do it for free. People said that they had success with different ways to get the solder to melt and readhere the chip to the board....turning it upside down and putting in a blanket so it would heat up and melt the solder to the point of resealing it, or taking the board out and putting it on balls of aluminum foil and baking it in the oven for 15 min, or just going to an apple authorized service center and having them resolder the chip on the board.
I AM NOT TELLLING YOU TO DO ANY OF THE ABOVE, AS I HAVE NO EXPERIENCE WITH THEM. But, before you shell out lots of money to replace the board, you could try these things, since you would have nothing to lose at that point.
Good luck with apple, hope they just do it for you free.