Remove power, battery, press hold the power button for the full 60 seconds. Release the button, slip in the battery, apply AC, count to 10 and try again.
If that fails it's probably it's power or still another bad motherboard. I rarely see folk change the motherboard due to the cost from Dell. And those ebay units always seem dead.
I have read several posts about this but none seem to be exactly the same as my problem, so forgive me for posting again. Laptop was on working fine, I left it for maybe 20 minutes when I come back to it, it was dead. I tried powering on again but nothing. I tried a different power supply and tried with and without the battery. Same result. When plugged in I get the battery light flashing to indicate there is power, the power light on the supply is also on. When I push FN and power, I get NO lights in the Lock LED's and the laptop dies in seconds as does the power supply, the led on the power supply goes out instantly, I have to unplug it, leave it for a few seconds then plug it back in and the power supply led comes on again. The only LED on the laptop that flickers for a second before dying is the wifi. Laptop is about 4 years old and is out of warranty. I look after it really well and haven't replaced any parts recently. It's on a docking station and never moves anywhere. (I have done all tests off of the docking station and directly connected to the power supply) I was advised it was the Motherboard but I have replaced this and it made no difference, I still have axactly the same problem. Any other ideas anyone please?