My 05 jeep wrangler x had a dead battery, jumped it, ran it, next day, dead again. bought new optima red top battery, started and ran fine but the next day dead again.

Sounds like you need to have your alternator checked.

I had the same problem on my jeep, clean and tighten the battery posts an d terminals. I did the that and it stopped.

Does the alternator light come on before you start the vehicle..
If not the alternater is incorrectly connected or the globe is blown . It will not charge if the globe is faulty.

Please check all of the engine grounds and body grounds including the battery cables

Not 100% sure why, but long story short, you need a new alternator mate.

Change your fuel pump

Ignition control Module out again? Over energized?

if you have an electric fuel pump that would explain the hum. unhook your incoming fuel line and blow the line clear, sounds like you've got some junk in your tank.it'll build up on the screen in the tank then fall off (at least partially) when your making turns or hitting bumps or holes. next time it's only got a gallon or so of fuel i'd drop the tank and check the pickup tube inside. sux but that's the only way to get to it. while you've got the tank off and out from under the jeep, might as well clean it out real good and replace anything inside (usually the screen) that doesn't look right, dirty etc. wouldn't hurt to run a bottle of fuel system cleaner in the next full tank of fuel either. preferably as soon as you put your tank back. good luck

are you sure you bought the right timing chain and gears? if the chilton says one things and you count differently then you could have bought the wrong set . just something to consider is all

On MY jeep, the Security Lockdown system kicked in, and it would not start at all, until I put the key in the door, and locked and unlocked it 5 times. I felt stupid, but it worked! A guy at the dealership told me, b/c he owed me a favor. He said usually it is a wrecker call!