Welcome aboard!
Getting to the keypad is relatively easy. These pics are for the passenger door but the driver door is the same.
Make sure the window is in the fully down position. Start at the bottom, indicated by the yellow arrow and pull the weatherstripping in the direction of the red arrows. Work your way to the top of the door. It comes out & goes in pretty easy:
There are four screws holding the pillar in, indicated by the red arrows. You can't see the bottom one in the picture, but it's there! Be very careful taking the screws out, you don't want to drop them in the door. Maybe use a magnetic screwdriver:
Once you get the screws out and start to remove the pillar trim, you will see how to remove the keypad.
I had similar electrical issues with my 02 xlt. The dome lights would stay on until the battery saver feature turned them off, the accessory delay wasn't working, the driver side puddle light didn't work, the keypad on the door would set off the alarm when I pressed it, the door ajar light would flash and beep at highway speeds, the radio would shut off as soon as I turned the key off, etc. Most recently all 4 windows stopped working.
Your issue could also be related to broken/damaged wire(s) in the boot. A lot of electrical issues can be traced back to broken/damaged wire(s) in the boot between the body and the driver's door. I found 2 broken wires and repaired them. The thin black ground wire was broken and after repairing it all was back to normal. When the windows stopped working, I repaired the thick black ground wire and the windows now work like a champ.
Here is the thread for removing the door panel:
http://www.explorerforum.com/forums//showthread.php?t=303524
Here is a great thread for checking for broken/damaged wires, thanks to
synyster for this awesome write-up:
http://www.explorerforum.com/forums//showthread.php?t=270081
Be sure to take your time when looking for broken/damaged wire(s). Check all the wires for breaks/damage. When you think you're done looking, look again, and again, and again. A bright flashlight can be very helpful.
Good luck and be sure to keep us posted.