Thanks for your help guys, I thought I would do a follow up to share my experiences. The good news: I fixed the rattle! Since I couldn't find any decent tutorials on the internet about fixing these door rattles, I decided to create my own. I also posted it at 9thGenCorolla.com, but here it is for you guys too.
Thanks again!
-M
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If you have interior door rattles and want to fix them, I diagnosed and fixed mine this afternoon. It's pretty easy so I'm not sure why I'm posting this, but I was a bit scared to pop off my door panel. People here don't seem shy to play with their cars but hopefully I can encourage someone less confident to do the same. Rattles are annoying and make driving my Corolla less enjoyable. Now they're fixed!
Two things: I have a 2004 Corolla S with leather trim and power windows. Secondly, the directions are almost identical to the Hayne's manual but with better pictures and more explanation.
https://i273.photobucket.com/albums/jj237/M...os/IMG_0627.jpg
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1) Disconnect your negative terminal from your battery.
2) If you don't have a trim removal tool or thin putty knife, you can do what I did. Take the end of a large flat head screwdriver and tape it a few times. I used duct tape because it was handy. Taping it will help prevent scratches on the plastic.
https://i273.photobucket.com/albums/jj237/M...os/IMG_0630.jpg
3) Gently pry off the power window switch panel using your trim tool. It doesn't take a lot of force as it's only held on by one clip.
https://i273.photobucket.com/albums/jj237/M...os/IMG_0632.jpg
4) Disconnect the power connector from the window switch. I had to use pliers to gently wiggle it out of the connector.
https://i273.photobucket.com/albums/jj237/M...os/IMG_0633.jpg
5) Inside the door handle you will find a small plastic cover that can be swung open by a flat head screwdriver. Open the cover and remove the screw.
https://i273.photobucket.com/albums/jj237/M...os/IMG_0637.jpg
6) Using your trim tool, pry the arm rest off by working around the edge. It's attached by two clips and might require some force.
https://i273.photobucket.com/albums/jj237/M...os/IMG_0639.jpg
7) After you've removed the arm rest, two screws will be exposed. Remove and set them aside.
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8) The door is now only being held on by 7 clips. Using your trim tool, start at the bottom of the door and work your way around until you've released all 7 of the clips. These don't take very much force to release.
https://i273.photobucket.com/albums/jj237/M...os/IMG_0643.jpg
9) Once the clips have been released, the bottom of the panel will be loose from the door. At this point the panel is just hanging by a lip near the edge of the window. To remove the panel, simply lift it upwards.
https://i273.photobucket.com/albums/jj237/M...os/IMG_0644.jpg
Once the door panel is off, you can inspect it thoroughly and get a feel for what could be causing your rattling. In my case, there were a few factors for consideration. First, one of the 7 clips fell out of the bottom of my door during the removal process because it wasn't connected. That was a possible source for the rattle since the panel wasn't properly attached to the door.
Secondly, my car has custom interior (which was probably the cause for the push-type clip being loose). This meant that the trim panel wasn't properly secured. The trim panel attaches to the door panel with 9 screws and washers. On a whopping 4 of my screws were loose to the point that I could spin the washers. Once I tightened them all, the rattle was gone and could be verified by hitting the door panel while holding it in my hand.
https://i273.photobucket.com/albums/jj237/M...os/IMG_0646.jpg
Here is the trim panel screws with the washers that were really loose on my car:
https://i273.photobucket.com/albums/jj237/M...os/IMG_0653.jpg
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There are other potential sources of rattling. On cars equipped with power windows, the cables are retained to the door by wiring clips. Check these to see if they're loose as there's many potential locations where rattling could occur. The cables for the door handle and door lock are also potential sources of rattling because they're in very close proximity to the metal on the door.
https://i273.photobucket.com/albums/jj237/M...os/IMG_0648.jpg
Reverse all the steps and put it back together. It took me 45 minutes from start to finish to take the panel off, diagnose and fix the problem, and put it back on. Just don't forget to plug your battery back in.
-M