Laptop won't boot

I am troubleshooting a Toshiba Satellite A135-S4467 laptop that won't bootup. It begins the boot process but eventually shuts down. Sometimes it happens before the login screen and sometimes after you've logged in, but always before you have a chance to use the laptop.

Windows Vista

Here is what I have tried thus far:

1. Attempted Safe Mode with same result on many occasions
2. Attempted Windows System Repair (and it attempted to implement a system restore point at one time) with same result on many occasions.
3. Took out 1 stick of RAM .. no luck. Swapped out for other stick ... no luck. Used other stick of RAM in other slot ... no luck.
4. Reset motherboard (removed battery & AC Adapter, hold pwr button for 15 sec, plug in AC Adapter WO battery, power on)

All with the same end result. Prior to this problem, about 7 months ago, I did run a Ultimate Boot CD and run thru diagnostics and everything passed. But, then, and since then, it has run very slow and sluggish and I always felt there were issues somewhere. So, in January, I set it back to factory settings (built-in image). It may have run a "little" better, but never as expected. Now, here we are. I have a hunch, it is a motherboard issue.

Are there any other quick/easy things to try? I don't want to take too much more time given this laptop only has a market value of ~100 to ~150 now.

Thanks for any help.

Sounds like it is overheating and shutting down to protect itself.
Might just need the dust and junk cleaned out, or new Artic 5 or the like under the heatsink assembly.
Actually I wonder if the heat sink fan is even running come to think about it.

I considered that for a moment, but this behavior occurs even when it is cold (after being powered off and unplugged from AC overnight).

Well it only take about 0.015 seconds to overheat a cpu.

Hhhmmm ... okay. All else being equal and no other hardware issues ... even if the heatsink is seated well and/or the paste is dried up, this is possible? I would've thought it would take at least a few minutes if not more. I'll open it up and take a look.

It is shocking just how fast a cpu can heat up.