I have an HP Pavilion dv6 laptop, with an i7 3rd generation processor, 8GB of RAM, a Nvidia GeForce GT 630M graphics card, and it is running Windows 64 bit.
It can run League of Legends completely fine but when my team is winning and we start attacking the last two enemy turrets, around that time my computer will completely freeze up. I have to turn it completely off and back on to use it again. This happens about 50% of the time now.
There is no way that it is overheating as I play with it on a cooling mat, and the computer does not feel hot.
As a side note, when I log back in to League of Legends and check my recent games, it has the game that my computer froze up in listed as a win, with all my stats and experience earned.