Studio 1555 will not charge or run on battery

I have had my Studio 1555 for about four years without any problem. Suddenly last week I found that it will not run on battery.

The battery appears to be about 30% charged.

It runs fine on mains power but when I turn it on it seems to try to charge the battery for a few seconds but then the battery symbol in the system tray stops moving.

If I hover over it the message says it's charging but after three days it appears to have charged only another four or five percent.

If I turn off the mains power the laptop immediately dies. It doesn't even try to run off the battery. I checked the battery charge with the LED's on the battery itself and this seems to confirm the battery to be 30 to 40 % charged!

Does anyone have any suggestions what the problem could be? Is this a failing battery or is there something more serious wrong with my laptop.

I'd be grateful for any suggestions.

Many thanks