A common issue when MySQL versions are upgraded is the presence of depreciated commands in /etc/my.cnf that would prevent MySQL from restarting. Other than the presence of depreciated ones, incomplete commands too can cause the issues.
When MySQL is upgraded to 5.5 from 5.1 or so, you might see that the service doesnt get restarted. Looking at the configuration file at /etc/my.cnf do you find something like this ?
slow_query_log_file
Here the path is not referenced, which is the issue confronted. Usually if slow_query_log is enabled in the configuration, then the path to log file should be mentioned, like :
slow_query_log_file=/path-to-file
Either comment off the incorrect line or if you are depending on slow_query_log mention the path to the log file as shown above. Once this is given, your service would restart fine.