In a medium saucepan bring the water to boiling. Add barley and 1/2 teaspoon of the salt. Return to boiling; reduce heat. Cover and simmer about 40 minutes or until barley is tender, stirring occasionally. Drain and set aside.
Meanwhile, in a 12-inch skillet heat oil over medium-high heat. Add onion; cook and stir about 5 minutes or until tender. Stir in the remaining 1/2 teaspoon salt, the squash, broth, pepper, and thyme. Bring to boiling; reduce heat. Cover and simmer for 10 to 15 minutes or until squash is just tender. Stir in corn; cover and cook for 5 minutes more. Stir in barley and parsley; heat through.