I have a Gateway W650i laptop that suddenly stopped working prior to Thanksgiving. Days before the laptop was unable to power on, it would unexpectedly restart itself. Regardless if the laptop's battery or a/c adapter are plugged in, the LEDs show no sign of the laptop receiving any power. I've tried the ATX method of removing both the battery and a/c adapter, holding down the power button from 15-60 seconds, then replugging either the battery or a/c adapter, but nothing has worked thus far.

With the battery removed, power cord unplugged from the wall,but plugged into the laptop, hold the power button down for a minute. Plug cord back into wall, without re inserting the battery, boot up and see if that works.