James, I hooked it up to the 5v out and the ground (with the resistor & LED in the circuit) and it's not illuminating the LED at all.
Then you didn't wire something correctly. This VERY simple test should light the LED.
Two things to try:
1. Go back to my 5V/Resistor/LED/GND circuit. If you can't make one LED directly powered light up, there is a significant problem. Either the LED is backwards or you some bad wires.
2. Jack's simple sketch but, again, increase the delay from 1000 to 5000. Observe the difference.
Where did you buy the LEDs? Do you have a link?