Car won't crank on without a jump

I have a brand new battery, but my Jeep won't start. When I push the start engine button, I get 1 click and all dash board lights come on. I have to jump it for it to start. I took it over to Jiffy Lube who confirmed battery was fully charged and in good condition, so nothing is draining it. They checked alternator and starter and said no issues with them. I've checked the starter relay and even switched it over to a different one to see if that was the case. But nope, Jeep still won't crank without a jump. Once Jeep is on and running, everything appears to be working smoothly. What else could it be :( Maybe the starter fuse?? or Ignition switch?? Help!