Computer starts freezing/lagging when anything even remotely graphically intense occurs.

I just bought a new computer, a Toshiba Satellite. I got it for one reason only, some weak gaming. But every time something happens in a game I get 10 seconds of sliding characters, dropping health, nothing, then dying. I usually play league of legends, which is very basic graphics wise. I tried everything I can in game, including minimum settings. If I get close to 2 or more other players I get the sliding/freeze that i mentioned before. But say multiple people use abilities (that create items or colors), or something happens (like a character gets bigger in size) my fps drops, by half. The computer I upgraded from did not do this, at all. And it has weaker hardware. What could my problem be? Or would it be better to take it back to Officemax for a refund?