Hanged a battery in 2000 jeep cherokee, jeep started up and die after a few seconds, put old battery back in and the jeep started up and die again after a few seconds.

Corrosion, you may also have a DRAIN on the Battery from the RADIO, or a few other circuits that could have remained open. You need to put a Multimeter on it and see where the draw and pull the Fuse for each to determine where the Draw is coming from

check fuses and relays might have popped one when switching battery

We had similiar issue last year with my sons 2000 jeep-
diagnosised crank shaft sensor ( repair code 320)- $79.00 part/$75.00 labor. Hope that helps.

Adjust the ignition switch on the column underneth

Have the alternator and the battery tested as one if not both items may have gone bad.

First check battery condition, second was the syc set after install?

pop in to auto electrician for a battery test they rarely charge you for this service to see if your battery is holding charge your average car battery has a life span of around two years next on the list is the alternator doing its job properly start with battery and take it from there

check the solenoid and the wires going to it

I am going to assume that it will not run even if you push on the accelerator pedal?
Can you install or attach an old timing light to the spark plug wires, turn it one and try to start it. The light should flash with the engine running, but if it shuts off at time of engine die, and the engine is still spinning, you are losing spark, My suggestion is the cranks shaft sensor on bell housing.
Second, install a pressure gage on the test port on the fuel rail and watch it as you start the engine, fuel pressure should not drop as the engine dies, if it does, the pump is not working correctly. There are two modes of power to that pump, one to start and timed, for only a few seconds to prime the system, and one to run continuously. Find the wires going to the pump at the tank. Connect test light to those wires and watch what happens during crank and at stall, You should not have the pump shut off and the engine dies.
If you have spark, and fuel pump working, when did you last change the filter,,but I put that LAST.
It has to be one or the other of these.
Good Luck