Satellite P305D S8828 Won't Boot.

Question

I have this issue with my laptop and I've seen plenty of others with the same exact issue except I've found no solution so I'm finally going to ask. I have a Satellite P305D that will no longer boot at all. Hitting the power button enables all lights and they stay on until I hit the power button again, that's it. The machine instantly goes off when regularly you know you'd have to hold the power button for a few seconds until that happens. There is no welcome screen as the screen backlight does not come on (I don't think it even powers up), the CPU fan momentarily spins then stops, such is the same with the hard drive and optical drive. 
Before I go any further, I'll first help you guys to help me (thus helping anyone else with this issue) by stating the things that I have done and have checked:
1. The battery works and is in pristine condition, it still holds charges.
2. The power adapter works and can charge the battery, I've checked the adapter connections for the motherboard and didn't see anything amiss. 
3. I've tried the [in]famous static discharge trick countless times(hold power for 20 seconds etc.)
4. Tried new ram sticks. Then alternated, then tried just 1 stick. 
5. Dismantled the entire thing upwards of 15 times and put it back together.
6. Reflowed the motherboard!!
7. Checked the processor, it still works.
8. Removed old thermal paste on processor and GPU and applied Arctic Silver.
9. It could probably go without saying but I'll say it anyway, yes the hard drive works. 
Now here's where things get interesting, prior to replacing the old thermal paste I put the machine back together after dismantling it and somehow it miraculously came on after pressing down in an area somewhere near the cable that connects the screen to the motherboard.
I was ecstatic except the amount of heat the thing kicked out of the side was insane and I was afraid of damage. So I turned it off and dismantled it once again, applied new thermal paste and put it back together now I'm back to square one. I've tried to replicate whatever in the world it was I did to get it to come back on prior but it didn't work as I wasn't completely sure what I did. 
I'd really like to fix it especially over buying a new motherboard because then I'll just be better off buying a new laptop. So I'm coming to you guys hoping that someone out there has the real solution to this surprisingly common problem that I've found no fix for. I greatly appreciate any help you can give me and I'm sure others who stumble upon this will as well. 

Answer 1

I have a P305 that is doing the same thing. I have done everything you have done except reseat the CPU (out of thermal paste).
Would love to know what part died. When mine quit, the LCD was working and the PC just quit responding. I got the "spinner" (not responding) on every application. I eventually did a hard reboot and that was the end of it. What surprised me was that the LCD no longer works at all. It WAS working when I did the hard reboot. I took it apart and removed the cmos battery and let it sit for an hour. I swear it acted a little different when I reinstalled the cmos battery -- but still no LCD. The cmos battery is good at 3.2 volts.
I additionally tried hooking up the laptop to an external VGA monitor. Still nothing.