Carefully disconnect your systems battery following this guide [guide|7511] Stoping at Step 4. Now press and hold the power button for 15 secs so you fully discharge the logic board. Now carefully plug in your MagSafe charger, press the power button, and then press and hold the ***T*** key. At which point you should see the FireWire or Thunderbolt Icon on your internal displays screen. Do you?
If not plug in your external display. Did you see it then?
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=== Update (10/13/2021) ===
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@tjones123 - Sadly your logic board has had it. This test was to see if we even can get the CPU's graphics engine to work. Someone with deeper skills might be able to replace the damaged components. In the end you won’t get a better GPU which is the weak point in this series.
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At this point I think your best bet is to replace the logic board. Now you could go for another 2011 board or what I strongly recommend is jumping to a 2012 board. This is one of the rare cases this is possible! Apple put a better CPU and GPU chip on the 2012 board. In fact I’m banging way on such a converted system right now.
Carefully disconnect your systems battery following this guide [guide|7511] Stoping at Step 4. Now press and hold the power button for 15 secs so you fully discharge the logic board. Now carefully plug in your MagSafe charger, press the power button, and then press and hold the ***T*** key. At which point you should see the FireWire or Thunderbolt Icon on your internal displays screen. Do you?
If not plug in your external display. Did you see it then?