My 2004 liberty won't start. i turn the key it hums, lights are very dim, and radio won't come on

You tried it in neutral but did you take it out of park and force it back into park? Just a suggestion since sometimes the switch that tells it that it is in park needs a bit of a nudge sometimes.

Possible solution - This happened to me and my battery was dead in my key fob and also I needed an ignition switch because a piece on it was broken which therefore wouldn't turn to start the engine.

have a load test done on the original battery as it appears that you have a shorted cell that is draining all the power from the jump battery.

I would check the fuses first.

You would need to check for voltage at the starter, the neutral safety switch, and the key switch. Sounds like the key switch may be failing.

Try starting in neutral. Gear sensor may be heating up and not registering park.

The 'Keyless Entry & Burglar Alarm System" is activated. You must 'Disarm' the system using the Keyless Entry Remove (Key Fob) to "Reset" the system. The reason the engine won't start is due to the burglar alarm - it has a "Starter Kill" circuit which is activated when the alarm is activated. The alarm must be DEactivated to DEactivate the 'Starter Kill' circuit.
Another way to start the engine is to get in the car, put the key in the ignition and turn it to 'ON" and wait 3 to 5 minutes until the emergency flashers stop/turn off. Afterward, you should be able to start the engine. NOTE: This does NOT reset the burglar alarm. It will go off again when you enter the vehicle without using the remote/key fob.

I would check your battery. I would also look for loose grounds. The clicking you hear is your fuel pump turning on. I would check your battery voltage and, have the battery load tested.

I found a paritally blown fuse. When the fuse blew metal pieces ended up partially making contact. After replacing the fuse everything worked great.

the solution for your problem is your starter went out. the price for a used starter will run at about 50 to 100 dollars and for a new starter it will run at about 150 to 175 dollars.