When you say that you tried flashing the BIOS once already, does that mean that the card is detected as a device that ATIFlash can flash when you use another graphics card to drive the monitor?
If so, I suspect your problem is the memory, rather than the core, but I don't think you'd be able to conclusively diagnose which one it is without help from AMD. You said in your other thread that you have access to a factory that manufactures electronics, so if you have access to a BGA rework machine, you might try replacing the memory chips with new ones. If that fails, maybe then try swapping the GPU out with a known good one, if you can.
You should make sure that any other regulators on the board are working first (look for SOP-8 packages), but that seems like your best shot to me, if all the regulators are working.
Its not really worth the hassle for a 360, but on a more expensive card, i would replace the RAM ICs with new ones and reball the GPU. If you have a way of testing the RAM ICs individually, you could maybe save the cost of new RAM chips by removing, testing and reinstalling the good ones, but as a mere mortal, I don't.