See page 58 for key operation
No discussion on dead battery enter.
http://www.fordservicecontent.com/Ford_Content/Catalog/owner_information/2014-Edge-U387-Owner's-Manual-First-Print_om_en-us_11_2013.pdf
OK different model but at least one other ford car owner is confirming that car will not open with key dead battery.
I suggest using a little effort on the key. Do not break the key!!!.
In the following forum the owner indicated a different feel as if the mechanical lock was maybe interacting with the anti theft system!!
I O course make sure you have the right key!!! whi knows keys can get mixed up.
Dead Battery Door Locks Inoperative Ford Fusion Hybrid
If the battery is dead I might consider searcing under the car for the starter motor battery connection and charging the battery. Least risk.
Opening hood with jimmy tool is possible. I would find a similar Edge and practice with the hood jimmy tool with the hood open before I would tear up the finish trying to open the hood
With the VIN number in hand I might go back to dealer and confirm key!!!
Good Luck
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