For people with following problem, the following Wiki article worked
well for 5.0.18_GA_3011.F7.FOSS. IE. Solved the problem.

Mysql Crash Recovery - Zimbra :: Wiki

Symptoms, following lost of power server restarted with
the following issues.
1) services OTHER then mailbox were running.
2) mysql would start but any write related request would result in socket lost error.
2) zimbra/log/mysql_error.log has multiple warnings of problems including thread dumps.
3) zimbra/log/mailbox.log the commonly seen error
"Caused by:com.mysql.jdbc.exceptions.MySQLNonTransientConn ectionException: Server connection failure during transaction.
Due to underlying exception: ' Connection refused'

best of luck..