My laptop is about 18 months old. I normally keep it on my desk with the power lead permanently plugged in but yesterday I moved it away from my desk and used it just with battery power (for the first time for some time) for about half an hour. When I put it back on my desk I plugged the power lead back in but didn't use the laptop again immediately. When I came back to it several hours later it had closed down, and when I pressed the on-off button the power light and keyboard lights came on for a few seconds (and then went off again) but nothing else happened. 

Since then I've tried several times to restart it but the same thing happens each time: the lights come on briefly and then go off again. If I hold the power button down long enough (half a minute or more) sometimes this happens more than once.

I've tried taking out the battery and putting it back in again (as recommended in another post on this site) but it hasn't made any difference.

I know almost nothing about the workings of computers, but this seems very much like a battery problem. I would have hoped for better performance given the age of the laptop, and its purported quality (however, I have become very disillusioned with Dell: the camera is also broken and one of the ports isn't working properly), despite the careful handling that the laptop has always had).

I'd welcome any advice on whether there's a good way to confirm whether I need to buy a new battery. I don't have a long time to spend on sorting this out: I need the laptop for my work, and if I need to order a new battery I ought to do It soon.