Minecraft turns on normally, singleplayer works, and even realms works. However, when I attempt to join a multiplayer server, I am able to join it for a few seconds, but then my client shuts down and the "Minecraft Quit Unexpectedly" screen shows up.
Your java installation is outdated.
This is a technical support issue; this site is for bug reports only. For technical support please use the Mojang Support Center.