CC3D has a power led that always lights up when there is good power, even if there is no / wrong firmware.
You can power it with either from your computer with a USB cable ("mini" connector), or with 5V power from and ESC or BEC plugged into any one of the 6 "3 pin servo / esc connectors" that poke up out of the board (negative/black goes toward the outside of the board).
Try a different USB cable or make sure your 3 pin 5V power is not backwards.
There is a different circuit for power from USB than from power from 3 pin, so try both ways in case one circuit is bad, but the other works.
Are you running Windows on your computer? When you plug CC3D in the USB does it beep and tell you it found something (in the improbable case that only the power LED is bad)?