Combine strawberries, blackberries, blueberries and raspberries thoroughly in a large bowl. Pour 3/4 cup of the mixed berries into a saucepan along with 1 cup sugar and water. Set aside remaining berries. Bring mixture to a rolling boil, then reduce heat to medium.
Stir the cornstarch into the hot syrup, stirring until it thickens. This should take about 2 minutes. Allow the mixture to cool completely and stir it occasionally for about 20 minutes.
Pour the sauce and berries into the shortbread crust. Place in the refrigerator for at least one hour.
