Re: "check charging system"
The simplest way I can think of testing to see if it is in fact an electrical problem (My guess) you can try hooking up some jumper cables to the battery with another car as if you were trying to jump a dead battery. If it starts right away then at least you know it is something with the charging system.
Since the car did start, it sounds like either a bad ground or a battery that's on the edge of being dead. Its not uncommon for a battery to come "defective" from the factory. If under warranty I would take the car in, but you can always look under the hood at the electrical connections. If you see any black marks around the connections its a sign of arcing typically caused by a loose wire.
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