Cut turkey into 1-inch bite-size pieces. Using a 3 1/2 or 4-quart slow cooker, combine turkey and mushrooms. Stir in water, salt, dill, and pepper.
Cover and cook on low-heat setting for 3 1/2 hours or on high-heat setting for 1 1/2 hours.
If using low-heat setting, turn to high-heat setting. Combine in a small bowl half-and-half and cornstarch. Stir into mixture in cooker. Cover and cook for 15 additional minutes. Stir in salmon and green onions.