650w NZXT PSU seems adequate for the Video card.
What is your motherboard model, ram type, OS, and are there any other hardware connected like hdd?
Some motherboards do require a 6-pin or even an 8-pin support power connector as well as the usual 24 pin mains power connector.
This video card requires a "PCI Express 3.0 x16 bus interface " which is rather new age for most motherboards.
http://www.amd.com/us/products/desktop/graphics/7000/7870/Pages/radeon-7870.aspx#/3
Also, Windows 8 is the preferred OS for this Vdeo card, not sure whether earlier Oses will recognise the utilization if PCIe 3.0.
It might still be that the PSU is not providing adequate power despite requirements being met. Itmight be that you will need at least a 750 watt PSU so that adequate power is available for the fans, however all the reviews state that it does draw less power than lesser models.
Try playing a game or watching a movie and then see if the fans begin to spin. It might be that they are spinning but are very quiet and you can't hear them whirring.
Upon further research, it seems that Windows 8 is the only OS that initially supports PCIe 3.0 but there is a fix for Windows 7 -
http://www.evga.com/forums/tm.aspx?m=1607292&mpage=1