Why did my lemon and penny battery fail? I followed instructions in Popular Mechanics publication for making a battery using lemons and pennies but it didn't work. I have a few ideas on why it might not have worked and would like to know which of them are more or less reasonable.

Here is what I did:


I used sandpaper to remove copper from one side of pennies to reveal the zinc core. Supposedly, only pennies minted after 1982 have a zinc core so I made sure to use only such pennies. The instructions call for 5-10 pennies - I did 6. 

Deviations from instructions:


I did not thoroughly remove all traces of copper from 2 of the 6 pennies. The amount of copper that was still visible covered less than 1% of the surface.
I used a lower grade sandpaper than the instructions called for. 

I cut cardboard discs slightly smaller than the pennies in equal number then soaked them in lemon juice

Deviations from instructions:


the cardboard discs I cut separated into three layers, the outer two layers appeared to be very tightly pressed and minimally absorbent

I made a stack of alternating pennies and lemon-soaked cardboard discs with the copper-side of each penny facing down. On the top of the stack I placed an intact, non-sanded penny then wrapped electrical tape around the stack. 

Deviations from instructions:


none that I am aware of

I attached an LED to the top and bottom on the penny stack. I tried both combinations of where to put the positive and negative ends but neither caused the LED to light up. 


Why I think it Failed:


By not removing every last trace of copper from the sanded-side of the pennies, I created a kind of short-circuit that discouraged the charges from moving through the stack of pennies. 
Since the cardboard was not very absorbent, it might have been particularly porous either and this might have prevented sufficiently free flow of particles between each penny in the stack. 
By using a relatively low number of pennies, I guess I set it up to have a relatively low voltage. Maybe I could have overcome problems 1 or 2 if I used more pennies.


I want to know if I my assessment of what went wrong is reasonable and welcome any suggestions of things I might be overlooking.
By not removing every last trace of copper from the sanded-side of the pennies, I created a kind of short-circuit that discouraged the charges from moving through the stack of pennies.
  


This is the main problem. Until all of the copper is gone from the zinc side of each penny, there is little reason for the two halves of the electrochemical reaction between zinc and copper not to just take place locally.  Your battery likely had one or more ionic short-circuits, just as you say, on these incompletely sanded surfaces.


  
  Since the cardboard was not very absorbent, it might have been particularly porous either and this might have prevented sufficiently free flow of particles between each penny in the stack.
  


This is unlikely.  As long as the cardboard was soaked through with the lemon juice, it should function fine as an ion-transport medium.


  
  By using a relatively low number of pennies, I guess I set it up to have a relatively low voltage. Maybe I could have overcome problems 1 or 2 if I used more pennies.
  


This is also unlikely. With five junctions (one between each neighboring pair of pennies), at a theoretical $1.1~\mathrm V$ per junction your stack voltage should have been at least about $5~\mathrm V$. This should be plenty to light a simple LED.