So the partition MySQL was mounted on ran out of space. As a quick fix, I decided to move mysql's data directory to /home/minecraft/mysql/. I then changed the datadir in the config to the correcy location. After doing that, it still wouldn't stary amd then someone mentioned apparmor. After changing the proper lines in the apparmor config, it still didn't work.
At this point I relized that I copied the files while MySQL was running, which most likely corrupted them. After removing the potentially corrupt files, I re-copied the files from /var/lib/mysql/. Still mysql would not start, it gave me a socket error and said it could not connect. I then tried to uninstall mysql completely, but when reinstalling Igot yet another error that reads:
Errors were encountered while processing: mysql-server-5.5 mysql-server E: Sub-process /usr/bin/dpkg returned an error code (1)
At this point I am completely lost and I have no idea what to do. I changed all the apparmor and mysql settings back to default now. I just need to get mysql back and running. It is apparently still installed, but only partially. This is the error I get when trying to remove it again: http://pastebin.com/Fc3gMCBn