Phone will not operate unless charger connected

looks like time for either a new battery or new phone.

 

Yes, your battery is completely shot. It sounds like the battery has reached the point where it is only able to deliver the voltage the phone needs when it is plugged into the charger (the phone itself cannot run off the charger: the charger charges the battery and the phone runs off the battery). The 2 options @ocnbrze gives you really are the only options you have.

 

New battery or new phone....
You make the choice