Thank you for your reply. Odds are this is what's happening, as it's much more likely there's a flaw in my wiring than in the Arduino. Can you explain what "sink the current" means?
There are two ways to power and light up a resistor/led string to a Arduino output pin.
#1 output pin > anode of diode > resistor > ground
#2 output pin > cathode of diode > resistor > +5vdc.
In number one if the output pin is high the LED draws current and lights up. The output pin is said to be sourcing current.
In number two if the output pin is low the LED draws current and lights up. The output pin is said to be sinking current.