You KNOW that the charging system is FINE? It sure doesn't sound like it. Even if it is, you have a power supply related problem and on an automobile the power supply is the battery and charging system.

Check your battery cable connections. Make sure they are clean and tight. Then using a simple Digital Voltmeter check the voltage across the battery with the engine running. If it is less than about 13.5 Volts then you do have a charging system problem.

Good luck,