My 2008 Ford Mustang will not start. Not making a cranking sound at all?

It makes one clicking noise when I turn the key. My dash lights turn on, my radio plays, my air conditioner is blowing air. I tried jumping it from two different cars but it still did not crank at all. I have NEVER had a problem starting my car, it always started immediately & ran well.
I took it to a shop and they are saying my computer is not reading my key. Is this a possibility?

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