They're either PCI_E power or Critical Core Temp warning LEDs ... so it's either a lack of power, a faulty PCI_e connection, overheating .. If things stay the same in a different system with an adequate PSU, then chances are it's a duff card.
List your specs as per the STICKY thread .. 
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AM3 965BE / Corsair H70 / 4Gb Corsair XMS3 2000Mhz / GigaByte 990FXA-UD5 / Corsair Force3 90Gb / x2 HD3870 Atomic Edition / x4 1Tb Storage & Momentus XT 250Gb / Sony AD-7700 DVD-RW / Auzen X-Mystique / Enermax INFINITI 650W / Lian-Li PC-7FNWB / Logitech X-530 / Logitech KBoard & MX620 / Logitech C525 / Epson RX685 / DELL U2312HM