" until I unplug the AC and then plug it back in - or remove the battery and then put it back in. "
Given the story I'd try another motherboard. I can't tell if you tried the other ideas such as removing the optical drive, just one stick of ram and NO HDD.
I've found a few machines I had to strip down and to use them I boot from USB (hint? I carry around Ubuntu on USB just for testing.)
My laptop started turning off last night randomly and I thought it was a heat issue as it was sitting on a bed and according to Speedfan my temps were a bit high (around 57 C) so I turned it off for a while and sprayed some canned air through the vents and then it seemed fine.
Today it started shutting off after being on for just a few seconds. I turn it on it starts up then turns off - at first it will maybe even get all the way into windows but then if I try again immediately after it will shut off in just a couple seconds - again seems like a heat issue because if I let it cool down for a while it will stay on for longer next time.
So I took it apart and blew air through the vents and fan, removed and reseated the CPU, took off the old thermal paste and put on new paste and put it back together. It booted all the way into Windows and I thought it was fixed - a minute later it shut off again and now is back to how it was before.
I have tried holding the power button while the battery and AC adapter are removed then plugging in the AC adapter only - doesn't help. I have also tried 2 different AC adapters and 3 different batteries - all of which work fine on my girlfriend's Dv6 - so I am sure it's not the battery or charger. I also tried removing one of the memory modules, then the other - no change.
Also, after it shuts off it won't turn on again until I unplug the AC and then plug it back in - or remove the battery and then put it back in.
What do I do next? Do I need a new motherboard or what?