Sorry that you are seeing this issue with MyEclipse.
Can you answer some more questions for us ?
1) How did you install MyEclipse ? Is it through Pulse / All-In-One Installer or Archived update site ?
2) Did you install any third party plugins lately which might have caused this issue ?
3) Clear the contents of the .log file which is located at <workspace dir>/.metadata/.log , replicate the issue and paste the contents of the .log file here for us to help investigate it further.
4) Switch to a new workspace, create a sample project and check if you can deploy and run it on Tomcat 6.
Let us know how it works for you.