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You say, with only display, it start and immediately off and without it it, stays on all the time and fan at full speed, if you have a short on lvds connector or cable this could happen, this why I asked you to try only with DP......
Aprendiz, thanks for the insight, but I think it stays on without anything attached because the power draw from HDD, optical drive, and backlight is more than what "it" can supply.
Run long or for ever without anything attached > with LCD > LCD + optical drive > LCD + optical drive + HDD (the latter almost unable to start off of a charger + empty battery).