Sreeram,
Sorry that you are seeing this issue.
Can you please answer some more questions for us?
1. Is the Eclipse running on the same machine as the MyEclipse ? Please share the MyEclipse Installation Details from MyEclipse > Installation Summary > Installation Details.
2. Can you please recheck if the firewall/proxy settings are set here Window > Preferences > General > Network Connections and are correct ?
3. Can you please recheck if the MySQL service is started and running at AdministrativeTools -> Services -> MySQL ?
4. Can you also please recheck if you are connecting to MySQL on 3306 port or changed the port?
5. If you are still seeing issues, please copy paste the contents of the .log file which is located at <workspace dir>/.metadata/.log for us to investigate further.