Voltage at rest won't tell you much about the battery's state of charge, it needs to be checked under load. Have someone measure voltage at the battery while you are cranking it - it should stay above 11v while cranking. Even over 10 will probably still allow it to start. If voltage stays high while cranking, your problem is likely somewhere else.
Get the battery fully charged and the have it load tested - this will tell you if the battery is bad or not. If the battery tests ok, then load test the alternator. If both check ok, you may have some other electronic issue that will probably require a trip to the dealer