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A couple of things to mention in addition; This is a "new" certified refurbished with new Dell issued Win10Pro key.
Service Tag: <service tag removed>
There are no blinking lights indicating an error code.
It sounds like the motherboard is probably faulty.
Does the system start up using battery power only?
If it does, do you get any LED patterns? (hold down the Fn key whilst powering the system on)
Does it still start up itself if you remove the battery and then plug in the AC adapter?
What happens if you attach power with all the memory removed? Do you get the same symptoms? (there should be memory located under the keyboard too)
If you could let us know, thanks.
If you're happy removing components, you could try disconnecting everything from the motherboard bar the CPU to see if the indicators change. (The system will/should power on just by adding AC power in this state: http://www.dell.com/support/article/us/en/19/sln18399/paid-diagnostic-faq-kb-article-322086?lang=en )
You could also try a reset of the RTC, removing the AC, battery and CMOS battery then holding in the power button to drain any residual power.
Did they tell you what they found? I'm having the exact same problem. Every detail is the same. However I have no warranty.