I just received my new GPU (Radeon HD 7750 Core Edition 1GB 128-bit GDDR5 PCI Express 3.0 x16) and everytime I try to turn on my computer, all of the other fans (CPU, PSU) turn except my GPU. I'm using an ASRock 970 PRO3 R2.0 motherboard and a Rosewill Stallion Series RD600 600W ATX12V power supply. There is also no display too when I plug in an HDMI cable into the graphics card and into my monitor.
Edit: I haven't been able to install/load any drivers and I've never been able to at least go to the BIOS settings.
I don't think that card has a secondary six pin power connector. Either it isn't seated properly (don't be afraid to push down with light force) or you don't have the drivers loaded. You need to load the drivers before installing the card. Last option is they sent you a dead card. You should be able to RMA it.