David, Here's an idea - There is a buffering action at the output pins of the IC which reduces the current flow. If your circuit (on paper) has an LED and a limiting resistor in series feeding from the output, the output voltage of the IC may be below the cut-off for the LED.
Try this - If your simulation software has a voltmeter or (better yet) an oscilliscope, connect it (on paper) to an output pin and see what you get. If you are powering the IC with 9 volts, the simulation sees 2 volts at the output and probably has set the LED cut-off at 2.1 or 2.2 volts (e.g., not enough to turn on the LED in the simulation). If your software does not have this feature, try connecting the LED directly to the output pin (without the limiting resistor) - bet it will work now.
Do not change your real circuit if it is working properly (I didn't really have to say that - did I?)