Sadly you have a bad GPU chip and the chip is no longer available from AMD. Some board repair shops may still have them but the cost of mounting a new chip given the value of the system makes this iffy.
Some people have tried heating the chip to revive it. Sorry to say this is nothing more than a last gasp of a dyeing system. You see, the design of these chips is what did them in, as well as us pushing them too far running apps that just where too much for them so the system overheats causing the GPU to breakdown faster. We fail to realize the timeframe these older systems were designed in and what great strides in apps over the last five or so years that these systems just can’t handle.
You could disable the dedicated GPU and use it with its Intel graphics engine while this will work it won’t be at the level this system was able to run.
The fact your internal or thumb drive won’t boot up is all related! As the POST is whats hanging. To prove this you can boot up under Target Disk Mode (you’ll see the FireWire/Thunderbolt Icon on the screen) then reboot and this time run your system in Safe mode. At that point you are running on the Intel GPU if you can get over the POST condition. Sometimes I had to do a SMC reset to get this to work as well.
Reference: Mac startup key combinations