There is a green light, top back of the processor by the plug that will not go off when powered down. I've disconnected from the power supply, reset the power supply and replugged. It still won't go off. I unplugged the power supply from the wall and unplugged the computer from the power supply; reset, replugged, powered up; it powers up fine, works well, but this light will not go out when it's shutdown, off or unplugged. What's this light for? Will it burn out? Is it a sign something's wrong? The computer works fine though. I am confused by this. Please can anyone tel me what is going on?
You worry for nothing about this diode You say it does not turn off even if the power supply is disconnected? But have you waited long enough while pressing the power button !? If it does not turn off either it is possible that it is the battery of the motherboard, which keeps it on, I doubt it a little, but why not! "Will it cause my computer's internal power supply to overheat overnigt?" you have an external power supply according to the product sheet, so no internal power supply, just maybe a button battery, but it is intended for!
Otherwise, there is no risk, you are talking about a computer, if it is this model:
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