Unplug the system and remove the base cover. Disconnect the battery from the mainboard.
Hold the power button for 30 sec.
Verify that the LED on the AC adapter is ON before you plug it into the system. If it's not, it's faulty - replace it.
With a verified adapter, connect the system. Leave the battery disconnected. If the system will then power up without the battery, plug in the battery. If that stops powerup, or re-starts the flashing LED, the battery is dead; replace it.
If the system still won't power up without a battery, the mainboard is bad.