Solution for reaching mysql:

 ** Increase Key Buffer ( yours is currently 64MB, but total indexes are 116M, so put at least 128MB). Should help immediately.
 ** Run mysqloptimize and mysqlrepair on your tables
 ** Increase table cache/ decrease total number of tables to increase the table cache hit rate. Maybe you've got some unused or old tables which could be deleted.

Other recommended confugration options:

   ** log_slow_queries = /var/log/mysql/mysql-slow.log
   ** long_query_time = 4
   ** log-queries-not-using-indexes

Check log file after some time.

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SET global max_connections = 1000000

show variables like 'max_connections'

mysql> show status like '%onn%';

mysql> show processlist;