Troubleshooting electrochemical batteries
Your experimental procedures seem to be perfect. There is just one minor error in your conclusion: you said that no current flowed. I disagree - current flowed, just not as much as you hoped. Harnessing one of these reactions to light up even the teeniest lightbulb would be similar to harnessing a bumblebee to a model airplane.

Getting a visible change upon connecting the battery is a reasonable goal. In one sense, you have already done it, by observing the needle move in the voltmeter. I know, you would like something more. A mechanical device might work well: say, a compass needle next to a coil of wire. When you connect the battery, some current will flow, some magnetic field will be generated, and the needle will move. 

Another possibility: if you take a small battery operated clock (either mechanical/quartz or digital) and remove the battery, you should be able to operate it with one of your batteries (you may have to boost the voltage). These devices use very small amounts of current, in the range that your batteries can provide.