Put a new battery in a 2002 jeep still will no turn over

carefully put a screw driver between the live on the starter and solenoid live with the ignition on if the engine doesn't turn check your earths from battery to chassey and engine are clean and secure

As long as it can fit in there, it should be fine.

you just need to relearn the idle hold your foot on the gas about 10-15%and let it run for a few min then slowly release the gas

Did you do a hard reset on the brain? Disconnect the positive terminal on the battery and leave it disconnected for like 10 min. then reinstall the positive wire to the battery. If that doesnt work then there are two possibilities.
1. The remote is faulty 2. The brain or reciever is faulty.
seek service or a new alarm.

I would check all battery connections. It sounds like you have a ground problem. If the motor is not properly grounded to body or battery is not properly grounded to motor and body, you can have all kinds of electrical problems. There is a ground strap from body to motor. Check to make sure it is not corroded. Sometimes it looks fine but it is corroded under the bolt.

first, though you mentioned no oil leaking, is there oil in the engine?
Next, if engine runs well and is not ticking or tapping, have the codes checked...most larger parts stores do this free. Once you have the stored codes you can look up what system is malfunctioning.
If engine is making any noise at all or there is no oil in it, DO NOT START OR DRIVE IT...make sure whoever did the oil change knows about this now...If someone forgot to put oil in, they may be buying you a new engine!
At this point it may be something simple but can also be very serious.(hope not)
good luck

Does the vehicle crank for extended period of time upon first starting? If so the fuel pump needs replacing.

Try going to the starter and check for battery power on the larger wire from the battery if that has power have some one sit in the truck and hold the key in the start position and check for battery power on the smaller wire if this has power the starter is junk try and tap it with a hammer some thimes they will start

Where is this fan located and what does it cool?

My wife had a similar problem with a 2003 Jeep Liberty. Her problem was that it stalled and she could not get it restarted unless it sat off for 30-45 minutes. It seemed like it was a problem with the alternator and battery but it had just gotten a brand new battery in it and we discovered the starter would roll over after the Jeep sat. We had it towed to the dealership and they replaced the Crank Sensor and the Timing Sensor and the Jeep now runs fine again. Side note: They charged us about $200 to fix these parts.