New battery not charging/not recognized by phone

My girlfriend’s (nearly three year old) iPhone 3GS started switching itself off prematurely a while back. First when the battery was getting low, then gradually sooner and sooner after receiving a full charge. It currently lasts for a couple of hours on a full charge. She ordered a new battery and the tools needed to open the iPhone and I installed the new battery, but all the phone does now is display the little plug symbol that you see when the battery is fully charged (instead of the zig-zag that says it’s charging), but it has no charge in it. The big battery icon on-screen seems to fluctuate randomly between empty (red), part charged (red) and half charged (green) when the phone is plugged in to the charger. It won’t work at all without the charger attached. With the charger attached it starts up and gets as far as the home screen but then switches off again after a minute or so, then goes through the start-up process again. It goes round in circles doing this infinitely.

To make sure that the phone itself was okay I put the old battery back in, which it recognized no problem. The battery charged fine and worked perfectly, except for switching off after a couple of hours, as previously, so clearly the phone is recognizing the old battery no problem and performing normally, except for the symptom of the battery reaching the end of its life.

The new battery has exactly the same three lines of text as the old one under the ‘Assembled in China’ line, while the line of numbers at the bottom near the gold stripe are slightly different. I’m guessing the new battery is a dud as the phone itself seems fine. Can anyone confirm before I source another replacement?