Sounds like your backlight is not lighting up. This could be either a bad backlight or a bad inverter. You will need a spare of one or the other in order to confirm which part is faulty. Fortunately the parts are inexpensive.
Inverter:
http://www.ebay.com/itm/Dell-Inspiron-1150-LCD-Inverter-Board-K02I048-00-/380750606918?pt=LH_DefaultDomain_0&hash=item58a6813246
Backlight for 15" screen:
http://www.ebay.com/itm/CCFL-Backlight-With-Wire-Harness-for-Dell-Inspiron-1150-15-LCD-/220821061304?pt=LH_DefaultDomain_0&hash=item3369f5feb8
Backlight for 14.1" screen:
http://www.ebay.com/itm/14-1-LCD-CCFL-Backlight-Lamp-Dell-Inspiron-1000-1100-1150-1200-2200-3700-3800-/220886648105?pt=LH_DefaultDomain_0&hash=item336ddec529