Chosen Solution
Using the iFixit website tutorial, I successfully installed a new battery in my iPhone 4s and the phone came back to life immediately with a battery charge of about 40%. When the battery charge decreased to 10% a few hours later, I plugged the phone into the charger to take the battery to 100%, but the battery will not charge at all. Is there a part in the phone that feeds the power from the outlet into the battery so it charges up?
Your IPhone 4s dock connector wouldn’t be connected check if it is connected that might help.
