There is a simple way to see whether you have a problem with your battery charging system. Remember when you turn the ignition key, there are three stops: stop I -power electrical system, and stop II, power fuel pump, and III-start engine. When you turn the key to stop II, you should see several lights on the instrument panel (including battery light). The battery light indicates battery charging testing system is working. Once you start the engine (and it is running), the battery light should go off which indicates battery charging system is working fine. Have you see any light on when the engine is running? If the light is off, your charging system is ok. If it stays on, your charging system has a problem (more likely the alternator). There are two possibilities for charging syste problem: bad alternator or bad regulator (which controls power flow to the battery).
Is your battery light on when engine is running?