It all had to do with a misaligned piece of rubber. Now I have an excuse to pry open the iPod.

1. Open the iPod and expose underneath the clickwheel
2. Move the little rubber piece to the center of the metal contact
3. Put everything back to normal and close iPod

The center button works fine now. The process took less than 10 minutes.
Well, I guess don't have to choose between a 120 GB 6G iPod Classic, 16 GB 4G iPod Nano, or 16 GB 2G iPod Touch just yet. Until the LCD or hard disk fails...

Keep on, Maple.