Agreed, also make sure you unplug any accessories you might have (ipod transmitter, garmin, ect) until you get that sorted. I fried my ipod transmitter with a problem like this.
Ended up being that the alt was not producing enough charge and I had similar symptoms to yours. Seemed like a bad battery but turned out it was just a weak alt.
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Whoever it was that thought it was a good idea to put the alternator on the bottom of the engine owes me somewhere around 500$