Will start/not start sporadically. When it doesn't start, doesn't turn over

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Battery has been replaced but didn't fix the issue. The problem seems to occur more often when trying to start the van after it has recently been run. (Stalled at the gas pump, in a parking lot after getting groceries.) When it doesn't start and the key is turned, the van has full power to all functions (including radio.) It's as if the ignition doesn't recognize the key is turning because there's no "pause" in electrical connection to any of the steering column. No engine light occurs, nor do any errors show up. I had it at O'Reilly and they tested a good battery and alternator.