Battery dying?

Hi there, I have an 06 scenic II which I think has an electrical fault. It won't start but starts, with jump leads, first time however after a few minutes driving the power steering goes, warning lights including a stop light come on. I toot the battery out and charged it last night put it in and it started first time however after a couple of minutes driving the low battery warning light came on and the steering started to get heavy. I thought it might be the battery but am I right in thinking that once started the battery doesn't do much so why would the car be dying? Any advice greatfully received.