So, I made something to test single batteries. It's crude and it's ugly, but it does exactly what I want it to, it works, and it cost me almost nothing. This one just does AAs, simply because I only had a single AA battery holder on hand and I mainly use those anyway. It can easily be adapted for different kinds of batteries, or more than one at once.
Here's how it works: You put a battery into a little battery clip, and if it works, an LED lights up. For that reason, it's going into the LED contest (*crosses fingers*).
(I made this without thinking to photograph it, so I'll recreate it with some diagrams and new photos.)
Step 1: Materials
1 NPN Transistor
1 Old AC adapter (preferably a lower voltage than the one I used)
Resistors in accordance with the voltage and current of your adapter (I used 2x 180Ω)
1 single AA batter holder (or other kinds, or more than one kind, just single battery holders)
A container of some sort (I used a flowerpot and some rubber rings)