Is it the compressor that has failed or the the bags that have failed. It's not uncommon for the airbags to perish if left for long periods. Also you'll need to look at the pipes and check for leaks. If you're sure it is the compressor then you may just have to look to replace it as often they are not a serviceable part.
you've not said anything about the specific system you have fitted but when you say "pulsing" what do you mean, compressors often pulse at a high rate as they pump up the system it maybe you're not used to hearing it as previously the car kept pressure in the system. with no pressure in the system it may be that it starts up the second you turn on the key. if it is a low/slow pulsing is it valves trying to operate to push air about, or is it the pump seizing up. So many questions to answer, where as at the moment the question you asked, is akin to "this doesn't work, why"