How do you turn off the water spigot outside After closing it full water is still flowing The only way you can stop the water is by using the shutoff valves attached below the handle Help?

Sounds like you have a bad valve. It would be best to replace the valve, most last a long time, but they do wear out. It is probably a gate valve, they are not that costly and are not difficult to replace. Before you replace the valve, you might want to check the rubber washer and/or seat within the spigot handle. Sometimes the washer will tear and will allow water to flow. Seats also wear in time and won't allow the washer to seal. Washers and seals are "a dime a dozen" and certainly much cheaper to replace than a new valve - also a lots easier to replace. Borrow a home repairs book from the library or do a google search on Plumbing repairs for detailed info on how to do it.