Drained battery will not charge when running

My battery was drained and when it started by jumpstart I drove it about 12 miles battery never charged was still drained. I took positive cable off battery when engine was running engine stayed on. Turned headlights on they were weak and drove it after I put pins cable back on battery. Lights stayed dim and battery didn't charge at all. Have a radiator leak when hot with belts on but alternator belt feel a bit loose spouts coolant out from steam and steams engine. Have radiator ordered just replaced water pump no more leaking from that. New belts but alt belt feels a little loose. Couldn't get the screws off the thermostat housing to replace with new one. What's making battery not charge?