Hey Youngman,
None of the errors you listed seem like they are anything critical that would cause the system to shutdown.
I'm just going to get you to re-do some steps that Mark44 did but I'll post some screenshots from my system so you know exactly what I am getting at.
First do this
Click Start> Right click computer> Select manage (This will open the Computer Management window)> Select event viewer> Windows logs> System
This is where windows logs the major errors like those that cause the system to crash.
Second, there's a lot of information we don't need here. Let's filter it.
Filter Current log...> Place checkmarks on Critical & Error> Click OK
Now we only see the major and critical errors on the system
Here's an example from my computer's logs. I'm looking back in Oct of last year, that's where I have some interesting errors. You will need to patiently go through this list. Windows corrects and logs plenty of errors that you never even knew happened. Start with the newest errors and work your way down.
The important bits of information here are the Source and Event ID, this will help is figure out what is going on.
Now what you have to do is go to
http://eventid.net/
This website is a good source to get an idea of what each entry listed here means and maybe get some help on resolving the issue
I selected the disk error I had. I type in the source and event ID and then click search. Then click on the "Comments and links for eventID from source" link and see what people have to say about it.
One more thing, have you flipped it around and touched the back panel to see how hot it feels? Since you're using a notebook computer here, there's a good chance that heat may be the problem. Most, if not all, newer computers come with a failsafe that kills the system if it reaches a specific temp threshold. Generally no user warnings. CPU hits 75C for example and poof! computer off.
If your computer is shutting down due to overheating, then the back will feel unusually warm. In this case, it's time to get a couple cans of compressed air, take the back pannel off and cleaning the dust. Also never use a "laptop" on your lap or anything else soft. You will block the air vents and nothing quite kills the lifespan of a computer like heat. (this is why I call them notebooks) Always use it on a hard surface like a table.
Hope this helps!
Cheers