I'm uploading a few closeup shots here of my circuit as I've assembled it. Ignore the color of the red and black wires I'm using to connect the top of my breadboard to the lower part. I haven't yet purchased blue and red Sharpie pens to color code the columns but if you're looking at the photos, the right-most column is positive voltage and the left-most column is negative voltage. I've also used wires to mimic the setup you see in Figure 4-34 so I can have a positive column running down the 2nd from the left side and a negative column running 2nd from the right.
I've also used my multimeter to check the 9V on the 100 microfarad capacitor at the top of my breadboard AND along the bottom - voltage is consistent across the entire breadboard. I also tested my LED again before rebuilding this circuit and all the segments that should light up are working.
At this point, the circuit is still not working. I substituted a 2nd 4026 chip and no luck. According to ACK Supply where I purchased these chips, they are Thomson Consumer Electronics chips - part # "CD4026BE RCA" - I wasn't able to find a data sheet on this particular chip with the Thomson name, but I did find this one from Texas Instruments. I'm assuming here (maybe incorrectly) that all 4026 chips are supposed to have an identical pin layout... but since I can't find one specific to Thomson chips, this may very well be my problem... but I'm guessing that it wouldn't make sense for different chip makers to switch around the pins. Again, maybe I'm wrong.
If you see a wiring problem, let me know... I used black wires to connect the 4026 chip to the negative voltage and red wires for positive. Green wires are used to connect all the other pins to the LED with the exception of pin 9 where I used a black jumper wire. I'm really hoping this is user error and that I'm just being blind to something really really simple... otherwise, I'm going to have to go and purchase additional chips from a different maker just to rule out bad chips or bad pin layouts.
For right now, I'm stuck...