Crash when playing for a few seconds

So... For a little time, I encountered an error, where loading a world and playing it for a few seconds resulted in a crash. Since the crash report said something about "java client depleted" or something like that...
I tried updating my Java version, getting the most recent one for Windows 7 64 bits... The one, I'm using... It resulted in the launcher becoming completly unusable, crashing immediatly when booted up. So, I proceeded to repeat that process, reinstall Minecraft and Java and also getting the new launcher... Now it's back to the beginning... I can start a game and choose a world, but then, it crashes after a few seconds. The game output is as follows:
"Error in class 'LibraryLWJGLOpenAL"
After trying again, it then read:
"Can't keep up! Did the system time change, or is the server overloaded? Running 2806ms behind, skipping 56 tick(s)"

Now, no tutorial, I could find proved to be of use here... So how can I fix this? What is wrong here?