thats probably the fuel pump your hearing. Is your alarm even capable of disabling your car? It might not be because you are able to push start your car. In my car if the alarm is on that thing ain't moving period.

Yes you can get your starter working again, first check to see if the starter is getting the proper voltage to it. Its a black wire I think, comes directly from the battery and goes to the starter. Make sure nothing is loose and that its getting 12 volts, i think it draws more voltage when its cranking but since you cant crank...

This problem dosen't sound very difficult if you know how to use a voltimeter. Have a mechnical friend come over to help you out