Sounds like a power supply issue but could be more. to further help,
when press the power button what color and condition is the light in the middle of the button.
Are any diagnostic lights lit
Do you hear the system fans and disks spin up.
Have you tried a different outlet.
Home Built Sandy Bridge P8P67 i7 2600k @ 4.5 GHz 8gigs GSkill Ripjaws. Corsair 800D Case and AX1200 Ps X-Fi Titanium Fatal1ty pro PCIe Sound Card
Dell Studio XPS 1645 Window 10 Pro

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