Is there a suspend/resume key combination, probably Fn+F8?
If you can output to an external monitor it sounds unlikely to be your graphics card. It could be 1. the internal connector to your laptop monitor, 2. the switch that powers off your screen when you close the lid, or 3. the screen display itself.
Check out the
Dell Support Website. There's a troubleshooting section for your make and model.
There's also a general troubleshooting guide for laptop displays (Information and Troubleshooting for LCD Flat-Panel Monitors and Portable Displays).
There's a user manual and, most useful, a service manual (how to take it apart guide) for your laptop.