How to determine if a state is a fixed point in a Hopfield network?
It's as simple as that.  Write out the state equation.  Substitute the state vector.  Verify that equality holds.   If it does, then you have a fixed point.

Note that what you're calling a state vector probably isn't one in the typical definition of that term.  The vector of neuron inputs is usually called the state vector. It would be unusual (though of course not impossible) for this to be all 1's.  

If what you actually have is the output vector, then you can solve for the state vector using the feedback function.  Then verify the resulting state vector is consistent with the outputs.  If so, then you have a fixed point.