Welcome to CC.
Make sure you have a current video card driver for Minecraft, I had OpenGL lag and crash issues with it on my laptop until I found a better driver. A quick check of the Windows error logs (in admin tools in control panel) wouldn't hurt as well, as you may have some random obscure issue that you can easily Google and fix, but only if you know what the error is. If neither of those help, you may want to try the MC forums, chances are someone else has had the issue, and eventually found a solution. I thought Minecraft itself also logged errors somewhere, but it doesn't appear to. Hopefully you can see the error it's throwing before your system completely borks.
If you like Terraria, I do strongly recommend buying a real copy, as that's made by a really tiny indie company (might even be one guy) that needs all the sales they can get so they can grow.
