What PSU do you have?
What GPU do you have?
What motherboard do you have?
Do you have another system around your home that you can install your GPU to see if it's working in another machine?
When you power up your PC, does the fans on the GPU spin, even at all? Also are their any lights or LED's on the card to indicate that is receiving power?
Have you also tried using a different 6/8/12 pin power connector? Is your PSU fully/semi modular? If so I would recommend changing the slot where you plug in the 6/8/12 pin connector if you can.
First off I highly recommend taking the GPU out of the PCIe slot, and making sure you firmly slot the card into the slot just to make sure it's seated right. I know you said you have done so already, but at this point you need to triple check. You probably know this, but make sure the monitor cables goes directly into the GPU, and not the motherboard.
Have you got another PCIe port on your motherboard that you can install the card in to see if you get a display? This will then helps us identify whether the card is faulty, or the PCIe slot.
Hope this helps.