Socket problems after upgrade

We just upgraded from 5.1 to 5.5 and seem to be having some weird socket issues. Here is the data I think is needed, let me know if you guys have any ideas.

First, here's the error message we're getting:

150201  1:32:59 [Note] Server hostname (bind-address): '0.0.0.0'; port: 3306
150201  1:32:59 [Note]   - '0.0.0.0' resolves to '0.0.0.0';
150201  1:32:59 [Note] Server socket created on IP: '0.0.0.0'.
150201  1:32:59 [ERROR] Can't start server : Bind on unix socket: Permission denied
150201  1:32:59 [ERROR] Do you already have another mysqld server running on socket: /var/run/mysqld/mysqld.sock ?
150201  1:32:59 [ERROR] Aborting

So naturally we went through and checked read/write permissions and as you can see the settings are set correctly, and no mysqld.sock file exists

$: ls -ld mysqld
drwxr-xr-x 2 mysql root 40 Feb  1 00:55 mysqld
$: ls -a mysqld
.  ..

We are using a different data directory and so we saw this thread: http://ift.tt/1D0r32c But after making the correct changes to apparmor it still does not seem to work.

/etc/apparmor.d/usr.sbin/mysqld

/usr/sbin/mysqld {
  /sc/mysql/ r,
  /sc/mysql/** rwk,
  ...
  /var/run/mysqld/mysqld.pid w,
  /var/run/mysqld/mysqld.sock w,
}

And finally, here is the my.cnf log:

[client]
port            = 3306
socket          = /var/run/mysqld/mysqld.sock

[mysqld_safe]
socket          = /var/run/mysqld/mysqld.sock
nice            = 0

[mysqld]
user            = mysql
socket          = /var/run/mysqld/mysqld.sock
port            = 3306
basedir         = /usr
datadir         = /sc/mysql
tmpdir          = /tmp
skip-external-locking
bind-address = 0.0.0.0
key_buffer              = 16M
max_allowed_packet      = 24M
thread_stack            = 192K
thread_cache_size       = 8
myisam-recover-options         = BACKUP
query_cache_limit       = 1M
query_cache_size        = 16M
log_error                = /var/log/mysql/error.log
expire_logs_days        = 10
max_binlog_size         = 100M

[mysqldump]
quick
quote-names
max_allowed_packet      = 16M

[mysql]

[isamchk]
key_buffer              = 16M

!includedir /etc/mysql/conf.d/

Also, although I knew it wouldn't work since mysqld isn't up and running, we did attempt to run mysql_upgrade to see what errors were coming back and this is what we got:

$: mysql_upgrade
Looking for 'mysql' as: mysql
Looking for 'mysqlcheck' as: mysqlcheck
FATAL ERROR: Upgrade failed

Any help would be greatly appreciated =) Lemme know if anymore information is needed.