Inserting Capacitor into CIrcuit causes LED to fade - Why?
As cowbydan stated, placing the capacitor in series to the LED will block DC currents. To achieve the desired effect of a glowing LED after removing the batteries you need a circuit similar to this : 







simulate this circuit &ndash; Schematic created using CircuitLab

The capacitor needs to be in parallel to the LED and the polarity of the capacitor needs to match the polarity of the connected battery. The resistor R1 is not mandatory in your particular application but it reduces the current which the LED consumes. A larger resistor value will increase the time the LED glows after you remove the battery but will also decrease its brightness. Just test it with some different values. Choosing a LED with a lower voltage rating would require a resistor in series to it to reduce the voltage.