BSODs some at random and other times while watching videos

Hello,
I'm new to this community and I hope someone can help with this massive issue I've had since March 10 of last year.

My pc is fairly new I purchased it one year ago. I got my first bsod the day I installed a video game called League of Legends. Since that installation I would get random bsod every few months when I would try and log off, then it would happen when I'd log on, then it would happen while I would try and watch a video on youtube or other websites.

Recently the bsod has become more frequent like 2-3 times per week, but now it seems worse b/c now it lags like crazy and my pc asks me to put in the recovery disc to bring it back to the factory defaults, which i kept avoiding for sometime.

But 2 days ago my pc lagged so much that I finally uninstalled League of Legends, but a portion of that game would not uninstall. But afterwards my pc lagged even more than before, then another bsod happened and i gave up and brought my pc back to an out of box state.

So I assumed everything would be better with LOL off my pc and it is as far as the lagging goes, there is none but to my dismay my pc Bsod twice and one of those asked me to use the recovery disc again. Which I have not.
Now I'm confused and frustrated and don't know what to do.

Btw I'm a bit of a newb when it comes to computers and such so pls give me thorough instructions and how to's thanks sooo much!

pc info:

model: Qosmio F60-126
Os: Windows 7 home premium
Bios: version 2.70
Cpu: Intel core i5 cpu m520 @2.40ghz
Video Card: Nvidia Geforce GT 330m

Please let me know what else you need.
 
Unfortunately I can't locate the mini dump files. I had to manually "activate" it in the Start up and recovery section. So I guess now you can't help me until I have another BSOD. :/ But thanks for your help anyway.
 
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