In terms of watts your psu is good. What brand is it? Some brands run better Amps than others of the same wattage. So, it's good that your system works without the card. Let's try this:
With the card in, cold start your cpu and go to bios. In Bios, if possible disable integrated gpu and turn on only discreet video card gpu (every board is different so the exact words aren't as important as the basic concept of turning on ONLY your 670 whatever the wording is). Save changes and exit to windows. If it fails, we know that the bios setting is correct so restart and go to safe mode for windows. In safe mode, uninstall your gpu drivers, restart, and go back into safe mode. (Please look up how to go into safe mode if you don't know already). Your card should try to take over the display and will flash a few times as it works through the process. It may prompt you to download and install the appropriate drivers; follow this. If you get to completion then something may have interrupted this process before; like an antivirus (actually make sure to have that permanently disabled while we are figuring things out; just remember to turn it back on when we are done!). Hopefully this works. Otherwise, it's most likely you need to replace this gpu. Please let us know how it works out for you! Stay patient and methodical and you'll get there! I think you're getting close! Hang in there, I know it can be very frustrating but find a way to make it fun! Best of luck to you!
Thanks,
Justin S.