leelambert,
Sorry that you are seeing this issue. This looks like an issue with permissions.
Can you please check if you can run the MyEclipse as Administrator and see if the issue persists ?
If the issue persists, then please provide the below information.
1. Please share the Installation Details from MyEclipse > Installation Summary > Installation Details ?
2. Does the Websphere 7 start without any issues outside of MyEclipse ? Can you please recheck the same?
3. Clear the contents of the .log file which is located at <workspace dir>/.metadata/.log. Now try starting the WAS 7 and copy paste the entire contents of the .log file here for us to help investigate further.