1) Your PSU could not be strong enough to handle the card so it just doesn't boot up, specially if works without the card it the PCIe slot and plugged in.
2) You install the 8-pin from the PSU to your GPU, correct and verified they were all plugged in correctly.
3) Your GPU is broken even though new (unfortunately we do at times receive DOA components)
4) Try turning off the PSU, unplugging it from the wall and hold the power button down on the case for 30 seconds. After doing that, plug everything back and try and start up the PC again.