I have the same year vehicle with the same engine. My car was exibiting the same issue. It would turn over a few times, then stop. Like the battery was dead. After much diagnostic, problem turned out to be the fuel injector. It went bad, stuck open, and filled the cylinder with gas. As everyone knows, you can't compress a liquid that much. Pulled spark plugs, turned over engine to expel fuel in cylinder, replaced plugs, oil change since fuel bypassed rings and got into crankcase, replaced bad injector.....Starts and runs like a champ. May not be your issue, but the symptoms sound the same.
Mine would turn over about four times, then stop. It would then refuse to turn over. If I let it sit for a few hours (during which time the fuel would leak out of the cylinder and into the crankcase) it would turn over a few times till the cylinder filled up again.
Check you oil and see if you smell gas. Pull your spark plugs and see if one of them is real wet. That will be your culprit.
Good luck.
