If you actually read the XenonLibrary page linked above, you'll see that dead GPUs on original models give errors 73 or 74 with secondary codes 1021 and 1022 respectively, and error 82 with secondary code 110(4)2 appears specifically on Xbox 360 S and E models.
Decompiled kernel code shows that Microsoft deliberately changed E74/1022 to E82/1102 on the Slim, likely so it won't be covered by extended warranty, but both of these errors are still caused by failed High Speed IO calibration between GPU and eDRAM:
Just because newer GPUs are more reliable and supposedly no longer have the flaw that killed off so many of the Phat units, doesn't mean they can't still die (again, it may as well be dead eDRAM which resides on the same chip).
Of course it would be great if there was a simple fix for OP's console, but considering what is known, there doesn't seem to be much hope for that, unfortunately.