Issues with Qosmio x505-q898

So a bit of background, I have been having several issues with my laptop. The first has been a severe overheating issue at times, though I was able to help solve the problem by using a laptop cooling pad for a time. Eventually though even that wasn't helping, and neither was trying to clean out the heat sinks using compressed air (I refuse to blow the dust back into the laptop). Being the laptop was already out of warranty, I disassembled the laptop down to the motherboard (which I have to say, thanks Toshiba for refusing to release any of your service manuals). I opened up the heat sinks, thoroughly cleaned out the heat sinks, reapplied thermal paste to both the GPU and CPU, and reassembled the laptop. Using Core Temp and a GPU monitor, my temps are well within normal operating range.

However, I am still having issues. Now when I start my laptop up, if my battery is plugged in and the AC adapter is plugged in, the computer will shut down without any notice within a few minutes. The lights on the LEDs on the front turn off (even though its plugged in) and will not restart without removing both the battery and power being removed, hitting the power button a couple times and plugging it back in. Now if I don't have my battery plugged in, it lasts a lot longer, but still shuts off periodically for no reason, and has to be unplugged and hit the power, etc. However, when I left my computer plugged in and running this morning (no battery), it sat there for a couple hours with no problem. I moved it onto my lap, and it shut off.

I'm curious to what some possible solutions to this could be. It's possible I reassembled it wrong (though everything seems to be working, all the buttons, etc), but it seems like something is causing the system to crash and lock out. I don't know if its software or hardware related, I'm considering reinstalling Windows to see if that helps, but I wanted to check in first to see if anyone else has a solution without going that far.
 
The motherboard is probably fried from the previous severe over-heating... Did you apply just a very small amount of thermal paste to the heat-sinks? Applying too much can act as a insulator. Were there any thermal pads used? if so, replacing them with paste is not a good move
 
Well I seem to have found the solution to the shutting down problem thankfully!

I was thinking that was the issue at first too, and yes, I applied a very thin layer of thermal paste. No pads on this computer, but if would point out the thermal paste was so dry it came off both the GPU and CPU with barely any coaxing, then cleaned it off with a paper coffee filter (hey, it's a cheap lint-less rag lol). I know too much acts as an insulator, so I was very careful about that (I work on industrial electronics at work and plan out every step of what I'm going to do before I do it, otherwise at work it's an expensive mistake!)

As I said, I ended up finding the solution out, and that was just leaving the battery out. It makes the computer very back heavy, but I remember now every time I started it without the battery plugged in before, I'd put it back in after it started working and not long after the computer would shut down. Since I left the battery out, I've been able to run games at full capacity with no overheating issues at all (both the GPU and CPU barely go past 70*C now! Way better than before), so I'm quite excited. I was a bit flustered before trying to find a solution, hence why I think I didn't recognize the connection between the battery and the shutting down issue.

I was reading this sometimes happens with bad batteries, has anyone else experienced this? I know it defeats the "purpose" of a laptop having no battery, but it doesn't bother me anyway as this computer gets too slow and doesn't last long without the battery anyway. More what bothers me is it constantly wants to fall backwards now!
 
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