To test the power adapter, unplug it from the system and plug it into the wall. If the LED on the adapter or DC side of the cable doesn't come on, the adapter is bad -- you will need to replace it. If it does come on,
1. Does the LED stay on when you plug in the notebook? If it goes out, you have a bad power jack or mainboard.
2. If it does stay on, unplug the system, remove the battery and hold the power button for 30 sec. Remove and reinstall both memory modules. Try starting up without the battery - if it will, but won't with the battery, the battery is bad.
If it still won't power up, chances are the mainboard is bad. Yes, Dell can still replace it - you can contact the Out of Warranty repair department for the cost.