My battery is dead. Why can't my charger charge them?

The charger is always outputting full voltage when disconnected. When it's connected to a battery with a very low voltage, it's almost like shorting the charger's output. This "short" causes the charger's overcurrent/anti-short protection to kick in and it shuts itself off. You'll notice that if you wait a short time the charger will come back to life.

The batteries are so thoroughly over-discharged that they initially try to draw a ton of power when presented with such a high voltage, which has the same effect as a short on the charger. The charger shuts off to prevent the cells from accepting the charge and potentially becoming dangerously hot while doing so.

A fast charger has greater short protection and so won't typically have this issue. You may need to open the unit up and charge the batteries individually so that they don't draw as much from the charger and cause it to shut down.