You have a 3-way pressure switch in your low-side refrigerant line. It is open when the pressure is below 27 psi and when above 350 psi (don't quote me on those values, but they should be close) and closed with the pressures are in between. Perhaps this switch went bad on you.
Otherwise, other than a wire open circuiting somewhere, it sounds like the A/C compressor should be active when you turn your A/C system on.
Otherwise, other than a wire open circuiting somewhere, it sounds like the A/C compressor should be active when you turn your A/C system on.