Battery will not charge?

Hi
I have a PushMeFon Mobile that I bought earlier this year for my wife's mum, who is in a care home. We've had recurrent problems with it not charging, and I have now brought it back home and tested it. What I've found is that when you turn it on, the three lights on the base come on together. Then the SIM and battery lights go out. Then the battery light starts flashing, and a few seconds later all the lights go out. This repeats until you turn it off. I have left it plugged in for at least 12 hours to see if the battery would charge, but there is no change. It looks to me like the battery is no longer able to take a charge. I've tested the output from the charger with a multimeter, and the voltage is correct at 5V. Can you help with this?

Thanks

Max Caines