Shut off for 5 minutes. Wouldn't turn over at all?

Drove van a few miles. Shut off for 5 minutes. Wouldn't turn over at all. Applied jump box(although battery is new) and it started, then died less then 10 seconds later. I was able to get it to start 3 more times after cleaning battery connections and checking connections at block ground and starter, but each time it died within seconds. Had it towed home. I can get the starter to spin by jumping it, but it seems that the starter relay is not firing. I swapped it with another I know to be functioning. The transmission range sensor appears to be working(the gear indicator and backup lights function properly).
Any suggestions?

Thanks.