After several years, the battery just would not hold electrons correctly anymore.
Followed the step by step directions on this site and they are spot on. The notes on lifting connector 1 and the gold grounding are very important.
After a little struggle with the screw for the camera, the phone is fully operational with a full charge.
It was be very helpful if the screw drivers sold were magnetized to hold the screws while trying to get them back in the holes.
I used a refrigerator magnet that is the shape of the iPhone and placed the screws I removed to ensure I put them back in the correct order.
iPhone 3G Replacement Battery
iPhone 3GS Replacement Battery
Phillips #0 Screwdriver
SIM Card Eject Tool