Latitude D520 screen goes black in first couple minutes

Last night when watching a video the screen went black.  I turned computer off and back on again and it will come on for about a minute then goes black.  An extrenal monitor works fine.  Also, if I leave the laptop on, close the screen and press on the top of the laptop, when I reopen it it will work again for a minute or two.  Any idea how to fix this?  The battery is dead and I do not want to replace it.  Could that have something to do with the problem?Thanks for any help.