Why do I get an error when I try to play?

That error generally means that your computer doesn't provide the 3D graphics support that Minecraft needs to run. If you're pretty sure you have the necessary 3D graphics hardware, you may need to update your video card's drivers.

You might want to look at the OpenGL support for your graphics card. This is different from DirectX support.

Maybe you'll find some useful information at http://www.intel.com/support/graphics/sb/cs-010479.htm

https://stackoverflow.com/questions/817216/is-directx-on-java-possible

Unless Notch uses JNI, he's not using DirectX. Considering that a lot of JNI code is not portable, and especially since DirectX doesn't exist on Linux and Mac without a lot of work, I'm fairly confident that your don't have to worry about it being your problem. You should be looking more towards OpenGL (if Minecraft uses OpenGL) or your Java Runtime Environment. Type java -version into a command window to show the version info. They are much more likely to be the culprit.