Well the error is telling me that the mysql service is not running.
Tell us a bit more about this system:
Is this a new install? If not how long has it been in production.?
Have you made any changes to the server since it last worked?
On to the issue if you open an command window and issue the following command.
ps -aux | grep mysql
Does it show the mysqld service running?
If not then issue the following command (sorry its in rhel syntax)
service mysqld start
or change to the /etc/init.d folder and issue
./mysqld start
To start the service will be distribution specific but the idea is to start the mysql server and see if you get the same results.