Acer Aspire 5750 No Power

I am in possession of an Acer Aspire 5750 that has a good power supply from the wall (checked with a meter) and has had the power cable that runs from the case to the motherboard replaced with a new checked (for continuity) cable.  When power is applied to the jack there is absolutely no sign of power being accepted by the Aspire.  No battery charge light, no response from the main power button when pushed, etc.  The thing acts like a brick.  I have inspected the motherboard for broken circuit traces leading from where the external power jack plugs into the motherboard and cannot see anything that a magnifying glass would allow my eyes to see.  This notebook has a history of having the black screen of death where it would charge the battery, respond the the power button being pressed, hard drive would spin up but absolutely no display.  It then proceeded to reach a new low by entering into this current state.  This is how it arrived in my hands for repair.  I haven't a clue what is wrong but the problem is so absolute that I feel I am missing something obvious to try and bring this back to at least a comatose state where I can try some things; like reflashing the BIOS.  Any ideas or suggestions are appreciated.  Even if the suggestion is to just recycle it as a lost cause.  Thanks.

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