Help whining noise

Hi peeps,

My mums pride and joy broke down today :-(

It started to make a whining noise when she turned the engine off. She thought it was the lamp post she parked next to at first. When she went to start it the engine wouldn't start at all and the noise was still there. The battery light also appeared on the dash.

My dad has bought a new battery and he says it seems to be running ok now but the noise is still there, he describes it as a buzzing/whining noise which is there no matter if engine is on or not.

It's a 2003 mini cooper.

Anyone come across this before?

Thanks