Minecraft locks up my computer?

I've been playing single player minecraft on my laptop. I got a gift code from my brother for it. We also play on a multiplayer server, but my net is acting up, so I've been playing solo. I can play for about 15 minutes before it locks up. And when it locks up, it TOTALLY locks up. I can't do anything with the machine, without doing a hard reboot. I've updated my virus software, done a system restore (but not to the point before I got minecraft), defragged, run Malwarebytes, everything I can think of. I tried uninstalling Minecraft, but it doesn't seem to be installed, just the icon on my desktop. Can anyone tell me what's going on, or at least how to remove Minecraft from my system so I can re download?