Yes…the video card/video hardware on Apple laptops is integrated into the logic board (not a part that can be easily replaced with a replacement part).
My understanding is…Apple (and many other computer manufacturers)…use lead-free solder…and lead free solder is not as "robust" as solder with lead in it. Over time it develop's cracks…and components fail. Video hardware (probably due to the heat generated)…seems to be a component that is affected most often.
Lead-Free Reliability Issues and Test Methods >> Evaluation Engineering
Even in the European Union (where environmental contamination issues are big concerns)…and where law makers actually pass strong laws to protect the environment. They still allow exceptions to laws to allow groups like the military and products in high reliability applications…can still use traditional (and more robust) tin-lead solder in their electronics:
Was Lead-Free Solder Worth the Effort?
Probably more info than you wanted to know!
I'll give you a more relevant computer example. I have a Early 2009 24" iMac that does have a "discrete" video card that is replaceable. I think that it is having video problems (maybe due to the lead-free solder issue). The big problem is…the replacement video card part that I need…can cost 50%-75% of the total value of the iMac.
So my point is…even if the video card part of your computer was replaceable…the part could be so expensive that it wouldn't be worth doing it. And since (in reality) the video part in this computer is not replaceable. Replacing the whole logic board is another solution…but in many cases can be even MORE expensive.
Believe it or not…there are some HIGH RISK DIY solutions…but these are HIGH RISK (could completely damage things). Which are called "reflow" methods. This is where the attempt is to "reflow" the lead-free solder. This can be done in at least three ways:
1. Stick the whole logic board in a home kitchen oven (get to the correct temp)…and the logic board is "baked & cooled" for the correct amount of time. HIGH RISK!!!
2. The video card on the logic board is VERY VERY carefully heated with a butane torch to reflow the video card solder. But again…this is VERY HIGH risk. And the possibility of damaging surrounding components is VERY HIGH!!! Especially if someone has not done it before.
3. There is a way that professionally trained folks use professional equipment to do things/repair. But this can be pretty expensive as well.
And beyond this…there are video card/video hardware problems that are NOT related to lead-free solder. Which nothing but a replacement video card or replacement logic board will repair/cure.
Again…probably more info than you wanted/needed to know!