Sorry for your issues. I know how it is to spend good money on stuff and have it not work is just infuriating.
Since you gave none of the required system specs for posting I will assume your PSU meets the requirements of this card and give you the benefit of the doubt. Absolutely double check that and if your PSU is at the bare minimum maybe you have an issue there.
OCCT from ocbase dot com is a great free utility to test all these components. I highly recommend you do that and watch to see if you drop bellow 12v.
That being said the fact the display doesn't initialize all the time at boot really isn't indicative of a power issue in my experience and would lead me to believe you either do have a card or monitor issue. I would absolutely test all ports if possible with each of your monitors one at a time if you can to see if you can isolate the issue down to maybe on gpu port.
That being said if you can't I have to think it is time to contact the support department for the company that made your GPU. They should be able to help. Maybe they have a new bios that fixes issues. Have other ideas or can offer an RMA to fix the issue. If you bought this retail and are in your initial return window exchange the card and see if that help. But test those other components as instructed first before doing that.
Report back what you find especially if you find what fixed it.
Again sorry for your trouble and Good Luck!