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I have a brand new IO board that I have tested with but I've got the ribbon connector on order.
Don't suppose the 13" air version ribbon could be used to test with could it? I know it isn't the same shape but I have one to hand is all.
I have found that if I plug the charger into another mac and get a light, then switch it to this one, weirdly I can get an orange light.
Also light or not, if I hold the power button for 5-10 seconds it powers up and displays fine but the fan is full speed and the battery isn't being seen.
Inspect cable and connector for corrosion. No idea if the 13" would work, compare the pinout of the connector between 3435 and 3437.
The battery not being recognized does not bode well for the SMC I'm afraid.