Four year old iPhone with dead battery :(
I used the iFixit online guide, along with the iFixit online video, and the iFixit tool kit to replace iPhone 3G battery. Although the repair/replace was a bit tedious, the iFixit guide and video made the steps clear and achieveable.
If you are not an expert, you can still accomplish iPhone battery replacement. Carefully follow the guide.
Note: After replacing the battery, my iPhone worked for three days, and then went dead again. I followed the iFixit guide and again opened the iPhone, where it was clear that one of the ribbon connectors had come loose. Apparently, I didn't have it seated completely. After checking each screw and ribbon connector again to make sure all were tight, I closed the iPhone, and after a few minutes it started right up.
After making any iFixit iPhone repair or replacement, give your iPhone extra time to start up -- I don't know why the boot takes a few extra minutes, but it does.