A hair dryer will not get the board hot enough to properly reflow the solder. You need a heat gun or a reflow oven. Generally temps of around 500-600 degrees F is enough to get the solder to become soft and "reflow (don't move the board till it has cooled down!!!!).
When using a heat gun for reflow, you want to go around the board about 4 inches above it and move in a smooth fashion, quickly, back and forth to heat the board up and prevent any kind of heat stress, then once the board starts to get hot to the touch (uncomfortable hot), start focusing on the GPU in a swirling motion about 4 inches above the board for about 30 seconds to a minute trying not to focus too much heat on any one area.
And before you proceed, I do not take any responsibility if you break your board. Proceed at your own risk!
This MAY work, but it may not either depending on if there is an encoder chip, fuse issue, video memory issue, and well, a many number of other things. There are companies based in the US that do component based repair if this doesn't work out for you. You can probably send it out for repair.