the problem is the backlight or inverter has failed. or could possible be the screen sensor. If its under warranty call Dell. We get a few in each week to fix like this.
regards.
Laptop Repair London
07758 941369
Specialist, January 2009
Send it to Dell for repairs if it's under warranty.
If it's not, remove the screen and clean the edge contact on the flat cable that attaches it to the mainboard.