initialize a vector in a constructor

The error is for the line

unsigned long myVector[N_ELEMENTS]

as N_ELEMENTS must be initialised during the constructor, the size cannot be known at compile time, late binding impedes this approach.

What you need is early binding.

template< const int i_Elements > class myClass{

  private:

    unsigned long myVector[ i_Elements ];
};

Instantiate an object like

myClass< 4 > m_Class1;

//rather than
myClass m_Class1( 4 );