sanjay,
well, this is a weird one, but it's clear what's going on. c3p0 is trying, but failing, to acquire Connections from mysql. The failure is what's unusual: the class com.mysql.jdbc.Messages can't be loaded, while other mysql driver classes seem to be loadable just file.
Here's the URL of a similar issue, but unfortunately no solution is posted:
http://mail-archives.apache.org/mod_mbox/tomcat-users/200603.mbox/%3C44071456.6030403@ste-energy.com%3E
You eventually run out of file descriptors because the driver has already opened a socket, but the thrown NoClassDefFoundError skips and internal cleanup and prevents a Connection from being returned, so no one can ever call close() on it.
I'm not sure what to tell you with this.
Here's are some suggestions: make sure there aren't somehow two incompatible versions of mysql's jdbc driver somehow visible to your application or tomcat. maybe download a fresh copy of the driver and tomcat, and try running your application from there, without any external CLASSPATH set (and ensuring that there is only a single copy of the jdbc driver jar files in your tomcat installation).
Do verify that mysql is installed and waiting for Conections. Prior to the NoClassDefFoundError, a CommunicationsException occurs -- maybe if you could prevent that from happening, the inability to load the Messages class wouldn't bite (though it's still bad -- and weird -- if unresolved). Try checking whether your app can connect to the database without connection pooling turned on.
Good luck!