@csdesign3 My best guess is the 5A power supply simply isn't strong enough to drive the iMac inverter plus the LCD driver board and other components. The success
@iMacConversionEnthusias had powering directly from the power supply, which was 8A size, may be confirmation of this. I think your power supplies trip offline due to the large current draw.
Considering the original A1312 iMac power supply units were 300-310W units and there were 5 main 12V power feeds that come from it, each one of those individual feeds would theoretically be capable of carrying approximately 4A each (leaving some power for lower power lines from the power supply). Since the iMac inverter uses 2 of the 12V power feeds, that puts the maximum potential inverter current feed around 8A. (see the math below)
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300W/12V=25A total power supply capability
25A / 5 main power feeds = 5A per feed
Subtracting some power from these due to lower power lines from the PSU (e.g., SMB connections) leaves approximately 4A per each main power feed
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Good engineering design would mean the normal inverter power draw would be around 60-70% of the maximum. So that means nominal maximum current for the inverter would be approximately 5A.
The above analysis would make sense as to why
@iMacConversionEnthusias had success with his 8A power supply and you did not have success with your 4A or 5A power supply. It would also seem consistent with some information that I have seen concerning conversion of the Retina 5K displays - they really push using 8 to 10A power supplies for those conversions.
What do you think? Everything above seems to make sense. I hope you are able to resolve it!