Tried to start my car and I hear is a continuous clicking noise.

I recently tried to start my car and I hear is a continous clicking noise. It sounds like it wants to crank to start the car, but nothing happens. Everytime I turn the iginition, the continous clicking noise lights up the instrument panel with the same amount of flicker as the noise.

I swapped batteries, but the noise remains the same and the car will not start. I replaced the starter and starter relay (both of which) I think are probably not at fault. Any ideas?