After driving why won't it start when parked that after waiting a half-hour it will start?

What is your question?

After driving any distance and parking with the engine off, the engine will not start again unless about 30 minutes has passed. There is no noise at all when the ignition is turned. I just replaced the battery. This does not happen after the car has sat a half hour or so. But does happen if I turn it off and jump back in the car 5 minutes later it won't start. Then I wait awhile and it starts. No unusual noises

What makes this problem better or worse?

Stopping and starting a short distance is when it happens even after the new battery

How long has your 2003 Jeep Liberty had this problem?

Just a few weeks