Pretty simple, open the remote...most likely just snaps apart, replace with same part number battery
Possible weak battery in the remote.
You might need to programming the remote. Their should be instructions in the users manual. You're remote could also be need new batteries.
Check instructions in the users manual.
Sounds like the contacts are still touching some how. Take the keyless apart and spray electronics contact type spray on the contacts and the points where the battery connects to see if this will help. Are you using a brand battery or a cheap-o?
I had the same problem. Google "keyless entry remote 2003 Jeep Grand Cherokee".
The keyless remote sensor for a 2002 Jeep Laredo is typically located in the front of the vehicle, near the rearview mirror or behind the front grille. It may also be integrated into the vehicle's Body Control Module (BCM), which is usually found under the dashboard or near the driver's side kick panel. If you're having trouble with the remote, ensure that the battery is working and the sensor is unobstructed.
Im not sure if you're talking about remote starters or alarms, but the alarm light did pop on when I changed the battery in my 95 Jeep GC Laredo. All I had to do was lock and unlock the doors a few times to reset the system.
centre top dashboard (red dome)
You have to program it with a DRB (Scan tool).
It is easy to do with online instructions. Just google "2004 Jeep remote programming"
If the key will not work in the door or the liftgate, you will need to call a locksmith or break a window.
dealer has to do it with factory scan tool