Forget the battery if not a laptop monitor. I found a posting that backs pyonir's capacitor posting. It is from Kioskea.net about a monitor that goes blank shortly after turn on, especially in the second paragraph:
Report Plato1123 Apr 14, 2010 5:48am BST
If your LCD display is turning itself off due to aging capacitors, an easy work around is to turn the brightness down! Brightness goes down, display draws less juice, and you can at least use it. As it warms up you should be able to gradually turn the brightness back up, although probably not all the way.
Sometimes this problem manifests itself as a display that turns itself off after a few seconds or will turn itself off and back on over and over again.