RadeonGate can cause all sorts of difficulties because the discrete graphics no longer work properly.
The MPB 15" and 17" models also have "integrated" graphics built into the CPU that don't rely on the internal discrete graphics.
There's a long-running thread here on how to DISABLE the discrete graphics so the computer can continue to boot and run on the integrated graphics only (with some limitations):
Force 2011 MacBook Pro 8,2 with failed AMD GPU to ALWAYS use Intel integrated GPU (EFI variable fix)
You need to take time to "read up" about this.
I'm not saying it is your problem, but it could very well be.
There is no real hardware "fix" for RadeonGate other than to replace the defective hardware. And the replacement hardware (not sure if it's just a daughtercard or a complete motherboard) will eventually fail as did the original.
I see you "just bought this" as a used item.
It's regrettable that you've been "caught" by this, I'd put that on the seller for not informing you of the issue first.
This was a MAJOR problem and issue with the 2011 MBP 15" and 17" computers.
Will the seller take it back?
If not, hope you didn't pay much for it. (sigh)