2002 Chevy Venture Won't Start

I drove our 2002 Chevy Venture yesterday, doing errands and such during the day with no problems. In the early evening I took my oldest son driving in it for an hour. Again, no problems. Two hours after returning home my husband went to drive it and it wouldn't start. No lights, radio, nothing. Completely dead. When you turn the key you hear a whirring sound (sorry, best description) but it gives no indication that it'll start. When I turn the key towards me, the radio will come on and the panel flashes Service Engine Soon. Would the battery go dead that quickly? Could that be the problem? Should we replace the battery before we panic and call a mechanic? We've only owned this van for two months, having bought it used. Any direction would be greatly appreciated.