Attach an external monitor and see if there's an image on it. If there is, the backlight has failed.
If the system appears to be running, it could be a video card failure. If there's no sign of boot-up, verify that the LED on the AC adapter is on before you plug in the notebook end. If it is not, replace the adapter.
Try reseating the RAM and powering up without the battery. If the system will not power up, the mainboard is bad.
Pop it out and insert it again. It's under a door at the bottom of the system.
If what you're saying is that the system won't power up, you've a faulty system board.
Most likely systemboard, but depends on a few factors.
Known good external monitor fails to display so, it IS systemboard UNLESS yours has a video card added in (Discreet) as opposed to built onto the systemboard (integrated). Just to verify, no POST/ BIOS display either at boot? If yes, then I would go for board (and vid card possibly). If you CAN see BIOS/ POST screens, boot to the diags.
When I plugged an external monitor in, nothing happened - but if I unplug it from the laptop, it pops up with the screen test (the same one you get when the monitor is turned on but the computer isn't). When I turn on the laptop, nothing ever appears on the screen - it stays black. And still when I hit the capslock or numlock buttons, those lights stay OFF. They light up momentarily as I boot the computer up, then nothing.
So it sounds like the system board? How do I fix that? And any ideas of cost, maybe? My warranty is up. Do I need to call Dell?