Inherited (and unlocked) an iPhone 3 GS from my sweetie when she upgraded, but it started showing these problems.
Symptom 1: Spontaneous shutdowns, when the battery was not depleted (50%+)
Symptom 2: "Dot" in the middle of the screen
Symptom 3: Screen assembly is being pushed out
Some online searching showed that the symptoms above are consistent with a lithium ion battery which has expanded--check out the shots of the screen being pushed out. The circuit board was being bent by the battery bloating--lots of force against the board when undoing the screws. However, after reassembly the iPhone works.
Screen + suction cup required a bit more force than I expected--maybe screen was stuck in the wrong position by the battery. I actually yanked out connectors 1, 2, & 3 by accident when removing the screen. However, they went back together all right.
It's a bit scary to figure out how the "flat" snap connectors work at first (I'm used to larger connectors), but they are pretty basic--you just push them together and they stick.
Getting the camera in its right spot *and* connected to the underside of the circuit board required a fair amount of finesse and an ample supply of foul language.