My jeep will not start.

Did you check the starter motor relay , location , under hood power distribution center ? When you turn the key to start the ignition switch sends a 12 volt input to the PCM / ECM - engine computer . The engine computer will then energize the starter motor relay . This is all computer controlled . Hooking up a scan tool to check for DTC'S - diagnostic trouble codes an viewing input data should be the first in diagnosing a problem like this .
040 Starting System Tests Start Here
048 Engine Hard to Start or No Start Scan Data for Starting Problems
How to voltage drop test starter motor circuit

Starter Voltage Drop

Likely that the "clicking sound" behind the dashboard is the IGNITION RELAY. Start by replacing the ignition relay (inexpensive and easy to replace).

the clicking noise could be a relay trying to latch or a security system armed either way you have to have your BCM(body control module ) checked, le me know what is the diagnosis

Your jeep ecu is in need of repair. It has what is referred to as the delayed check engine light problem. If you'll notice, next time you try starting the jeep, it will not start when the check engine light finally comes on, on the dash. The fuel pump will only come on when the ecu finally energizes the relays, and that's when all the clicking starts. Look on ebay for an ecu repair service.

I'll try this out. I had tried the neutral/start thing and even the remote start, but when it's bad, nothing happens. I do hear a relay click (I think under the dash, but that's it. It is at the dealer for the second time and so far it works fine every time they try to start it. We will try again tomorrow. They want to replace the starter and/or the ignition key lock. I want them to find the fail so we have to wait until it fails to get the codes. Aahhhh!

The humming noise you hear is the fuel pump. It is probably your starter soleniod. If you hear an electric click under the dash near the steering column when you turn the key then the ignition switch is ok and your starter needs to be replaced. This happened to me last month.

Check the brake light switch, located under the dash above the brake pedal. The other noise may not even be related to brake lights staying on

First, make sure you can turn the engine by hand. If you can't then the starter can't turn it either. Have someone else turn the key and look for the source of the click...may be a relay. Go over the starting circuit with a volt meter. Check for power at the starter main terminal and then with the key turned to "start" check for power at the trigger terminal on the starter. Check battery voltage and check relay operation.
You have a neutral safety switch on the transmission if its an automatic and a clutch switch if it's a stick. Check them as well. Make sure battery grounding on fender and block are also clean and secure.

Listen for a click from under the steering column when you turn the key on. If you hear no electrical click then your ignition switch could be bad. If you hear an electrical click the you starter soleniod is bad.