14.04 - Mysql 5.5 server not working

I had Ubuntu 14.04 installed on my system. I recently updated ubuntu and now my mysql does not start and workbench says that mysql server has been stopped. And when i try to start it gives me the following error

2014-08-12 23:02:04 - Checking server status...
2014-08-12 23:02:04 - Trying to connect to MySQL...
2014-08-12 23:02:04 - Can't connect to MySQL server on '127.0.0.1' (111) (2003)
2014-08-12 23:02:04 - Assuming server is not running
2014-08-12 23:02:04 - Server start done.
2014-08-12 23:02:04 - Checking server status...
2014-08-12 23:02:04 - Trying to connect to MySQL...
2014-08-12 23:02:04 - Can't connect to MySQL server on '127.0.0.1' (111) (2003)
2014-08-12 23:02:04 - Assuming server is not running

And also when i try to login using terminal (mysql -u root -p ) i get the following error:

ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)

I have also tried to reinstall Ubuntu but i am unable to do so. Gives me the following error:

Reading package lists... Done
Building dependency tree
Reading state information... Done
mysql-server-5.5 is already the newest version.
0 upgraded, 0 newly installed, 0 to remove and 4 not upgraded.

I have data which i have not taken backup of as i am unable to log into the server. I am a newbie please help me resolve this issue without losing my data.

Awaiting for your earliest response.

Below is the error message from cat /var/log/mysql/error.log

140813 21:22:50 [Warning] Using unique option prefix myisam-recover instead of myisam-recover-options is deprecated and will be removed in a future release. Please use the full name instead.
140813 21:22:50 [Note] Plugin 'FEDERATED' is disabled.
140813 21:22:50 InnoDB: The InnoDB memory heap is disabled
140813 21:22:50 InnoDB: Mutexes and rw_locks use GCC atomic builtins
140813 21:22:50 InnoDB: Compressed tables use zlib 1.2.8
140813 21:22:50 InnoDB: Using Linux native AIO
140813 21:22:50 InnoDB: Initializing buffer pool, size = 128.0M
140813 21:22:50 InnoDB: Completed initialization of buffer pool
140813 21:22:50 InnoDB: highest supported file format is Barracuda.
140813 21:22:50  InnoDB: Waiting for the background threads to start
140813 21:22:51 InnoDB: 5.5.38 started; log sequence number 80726593570
140813 21:22:51 [Note] Server hostname (bind-address): '127.0.0.1'; port: 3306
140813 21:22:51 [Note]   - '127.0.0.1' resolves to '127.0.0.1';
140813 21:22:51 [Note] Server socket created on IP: '127.0.0.1'.
140813 21:22:51 [ERROR] Fatal error: Can't open and lock privilege tables: Incorrect file format 'user'