Hi Dave and welcome.
Unfortunately, you cannot change the graphics card as it is soldered into the motherboard and not economic to replace.
If Sony do a repair, they will completely replace the whole motherboard - which is an expensive repair and not really worth the cost for the user to do themselves as you could probably buy a new notebook for the retail cost of the repair.
If things don't work out with Sony, it is worth investigating a "Reflow" or "Reballing" repair - try Google for details.
Good Luck.
