I had a issue just like this before and it turned out to be the coil. There is a test you can do to test the coil, not the method I describe below. I would test the coil and inspect the main relay. Without trouble shooting this more, we cannot give you a better guess than what commonly goes wrong.
Pull off one spark plug wire from any spark plug and put a spark plug in the wire. Then hold the spark plug next to a good ground like the engine. Have someone else turn the car over and check for spark. If you are not getting spark, then it is ignition related. If you are getting spark, check the main relay, just above the hood latch under the dash. Touch the relay and put the key to the ON position. It should click, if it does, turn the key to run. It should click again, sending a message to the pump. If you do not get these clicks, then you have a relay issue.