Could be either or could be a faulty connection. Check the voltage across the battery terminals, you should have about 12 volts, if you have but its still dead you have a connection problem, possibly the battery connections themselves or the earth lead to the engine.
If the battery is flat it could be the battery itself or the alternator, if you can get it running there should be about 14 volts across the battery if the alternator is OK.
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