Recently an issue was reported to me where execution of sharepoint configuration wizard was failing for addition of a server in an existing farm with the error message "Not Available locally". This was failing just at the step where the connection to existing configuration database is carried out. The logged in user had all necessary rights including them in admin and content database. After some initial investigation I though of starting the wizard as an administrator option by right clicking on it and selecting "Run As Administrator". We did it and thats it it worked.
I hope this will help you out.