Remove the neck and giblet package from the chicken and pull off the flap of fat if there is one. Rub hen inside and out with salt. Place the chicken in a pot that is just large enough to hold it and tall enough to completely cover it with water. Add cold water just to cover the chicken and stir briefly. Place in the refrigerator for 3 hours. Remove the bird and rinse for several minutes under cold running water to remove all salt inside and out.
While the chicken is in the refrigerator, make a simple stock by simmering the neck, giblets (no liver), 1 onion quartered, 1 leaf end of celery, 2 sage leaves, 2 thyme sprigs, and 1 quart water in a large saucepan over low heat for 1 to 2 hours. Strain and save the stock. Pull the meat from neck and add to the stock. Cut up the giblets and add to the stock.
Preheat the oven 475 degrees.
Arrange a V-rack for holding the bird over a pan to catch juices. Pour 1 1/2 cups of the stock into the pan, reserve the rest. Place the remaining onion, leaf ends of celery, sage leaves, and thyme sprigs, plus the orange and bay leaf, in the chicken cavity.
In a small bowl, stir together corn syrup and butter. Brush the chicken lightly with this mixture and place in a V-rack, breast side down. Roast 20 minutes, basting with drippings in pan every 7 minutes. Remove the chicken from oven and turn so that one leg and thigh are up. Baste with the butter mixture and return to the oven for 10 minutes. Remove from the oven again, turn completely over so that the other leg is up, baste well with the butter mixture, and return to the oven for another 10 minutes.
Remove from the oven again and turn the oven down to 325 degrees. Leave the oven door partially open so oven temperature will come down quickly. Turn the bird breast side up, brush well with butter mixture and return to the oven. Baste every 5 minutes. In 5 minutes, check breast meat temperature using an instant-read thermometer. The ideal temperature to remove it is 150 degrees to 154 degrees. If necessary, place back in oven an additional 5 to 10 minutes until it reaches this temperature. Breast meat temperature rises about 2 degrees every minute in the oven at this temperature.
Add as much of the pan drippings to the remaining stock as you can without getting the sauce too salty. Stir cornstarch into 1/4 cup cold water and stir it into the stock-drippings mixture in a large saucepan. Heat over medium meat, stirring constantly, until the sauce thickens.
Allow chicken to stand at least 15 minutes after removing from the oven. Carve or partially carve the chicken and arrange back in bird form on the serving platter. Pass hot gravy in a separate bowl.