1) If the battery is completely dead (no voltage at all at the terminals), it's disconnected because the charge got too low, and charging a fully discharged Lithium Ion battery can lead to things like fire and explosion.
2) Leave the charger plugged in for 24 hours. The first few hours the battery barely gets enough power to shut the phone off. It's called "ramp-up", and it doesn't put much charge into the phone.
3) For the longest battery life, charge the battery when it's down to about 50%.