Something else that is often overlooked is a completely drained battery. Usually they will not charge.
This can be rectified quite easily.
How we do this is as follows....
Before connecting battery or after you disconnect, check if there is power in it(even a small bit) if there is it should accept a charge.
However, if the power in it is 0.5 volts or less, it may, because of the diode accepting input current, reject the charge.
This happens purely because the low power ratio can not determine in the diode which is negative and which is positive.
Having the drained battery disconnected or at least the Positive(Red) wire, Using a PP3 9V battery and two wires Connect positive to Positive and negative to Negative for 5 seconds.
Doing this blasts a small quick charge into the battery and also determines the correct polarity.
Re-conect the battery, you may be surprized! this boost can revive many a dead battery.
If you are sure your battery is 100%, connections 100%, Display 100%, the next step back is your I/O button.(sleep)
There are 4 terminals on an iPhone battery. You should measure anywhere between 3.5 - 4.2 volts between the + and - terminals. The other 2 terminals are a temperature sense line and a data communications line.
Unfortunately, i do not have a 3g or 3gs in the workshop to answer your query. A miltimeter across the 2 OUTER pins will determine which is +.