2 amps for the overnight trickle charge. Something's screwy, though. If the battery actually won't turn the car over, and then after 5 minutes on the charger it will turn the car over, you've either got a bad battery, or, more likely, a connection problem. Did you check the terminals for good contact with the battery cables? Clean 'em off if they're the least bit schumtzy (use Diet Pepsi or Club Soda and a little steel wool to polish 'em), then put it on the charger overnight and see if the problem remains.
The battery light will go off once the engine's started because it's basically a voltage sensor. Your battery normally puts out 11-13 volts, depending on how healthy it is and how long since it's been charged. The alternator puts out around 14 volts, and the light's calibrated to turn off above 13.8 or so, so anything from whatever the minimum to light the light up to 13.8 gives you the light.