Reflowing won't work, it's a defect in the GPU itself. I recently went through a pile of those laptops and only the ones that had the revised GPUs worked. All of the others were bad. If Apple installed a new GPU, there should be a small green sticker on the RAM slot. You can also tell based on the part number and date code on the GPU, but that requires totally disassembling the laptop.
Having said that, your problem looks more like a bad LCD panel to me. Usually, a bad GPU causes no picture, random lines or blocks over an otherwise normal picture, or crashing during boot. Try it with an external monitor to be sure.