New battery but Jeep dies when I try to start

Almost sounds like a loose ground,but the battery and starter were both good the morning it stopped starting,maybe the ignition switch in the column is not releasing the full power to the starter?
Replaced the ignition switch and starter relay - still have the same issue
 
You have narrowed it down to a bad connection either in the positive or ground cabling.
Look for corroded and/or frayed cables. Corrosion shows up as a turquoise color on copper.
Make sure the ground cable is secure to engine.
All copper connections should be shiny, not black.
All connections must be tight.
Any cables showing above faults must be replaced.
Best of luck.
 
With everything going dead with a good battery I'd suspect a bad/corroded cable connector.
I used to work in an auto parts store many moons ago in Newark, NJ. We had a situation like this where a guy bought a new battery and was claiming we sold him a lemon. The store used to have a repair shop that had been abandoned. The owner was an old timer who had been working on cars for many years. He had the guy pull the car (Buick 225 Electra) into one of the bays. He removed the positive cable stripped off the insulation and the entire cable was corroded from one end to the other. Replaced the cable and the car fired right up with new battery that the customer was saying was a lemon.
 
Buy a new set of battery cables. Make sure the ground connections are tight.
Buy a cheap Volt-Ohm-Meter from Harbor Freight. Disconnect the battery and measure the resistance from the battery-end of the red cable to the starter. If it's more than a couple of ohms, the cable is corroded. Measure the resistance from the battery-end of the black cable to the starter motor case. If more than a couple of ohms, track back to find the bad connection / cable.
Good luck!