This happened to me and over a number of weeks the problem got worse. I took it to a shop to get it fixed and they told me it was the motherboard and that it would cost £135 - £180 to repair as you can pick new ones up quite cheap now I thought it wasn't worth it.
After looking for advice on the net some guy said it was due to his battery and adviced taking it out and using straight from the mains. Hey presto it worked. A new battery is £30 so that is a saving of £100+.
Michelle Butler, November 2009