Answer
Check whether the WebLogic startup script actually exists at the expected domain path for your project — if that file is missing, use Developer Studio's 'Reinstall Application Server Instance' option to regenerate the local WebLogic domain and its startup script. If the file does exist but the server still won't start from Developer Studio's own Start Local Server action, try running that same startup script directly from Developer Studio's built-in terminal to see more detailed output about what's actually failing.