The battery light should come on when the ignition key is turned to the on or run position and go off immediately the engine starts. If the charge light doesn't come on when the ignition is in the on or run position, or if the battery light doesn't go off when the engine starts and runs, or finally if the battery light flashes or stays on when the engine is running all these symptoms are signs of a problem with the charging system (usually the alternator). The voltage regulator, is located in the alternator and is most likely your problem. Put a volt meter across the battery at rest a fully charged battery should be 12.6 volts the moment the engine starts and runs the battery voltage should read approximately 14.6 volts or the alternator is not charging.
If the alternator is not charging all the electrical loads are getting power solely from the battery, the moment the battery voltage becomes too low to operate the fuel injection computer, ignition and fuel pump, the car's engine will stall.