Verify that the LED on the AC adapter is ON before you plug in the system end. If it's not, replace the adapter.
Unplug the system and disconnect the battery. Hold the power button for 30 sec. Remove and reinstall both memory modules. Leave the battery disconnected. If the system will start up on AC only, but won't with the battery installed, the battery is bad -- replace it.
If it still won't power up, the mainboard is bad. Replace the system board.