Minecraft Isn't Launching

Whenever I click "Play" in the launcher, it closes, and never launches Minecraft. I know it isn't just taking a long time because if I look into task manager I never see the Java program. I just got this computer and I've tried old and new versions of Java. I have no idea why it won't launch.

New Launcher Crash Message:

The game crashed whilst initializing game
Error: org.lwjgl.LWJGLException: Pixel format not accelerated

Old Launcher Crash Message:

OpenGL: ~_ERROR~ RuntimeException: No OpenGL context found in the current thread.