MY 2009 Mazda3 AC suddenly stopped working. Can't get compressor to kick on to check coolant. ANy suggestions

 

Check related fuses and wiring and replace if necessary. If good see about testing compressor connection to ground, continuity and ohm measurements if possible. If compressor burnout occurs u need to completely purge the system with nitrogen before installing a new compressor as well as replace filter driers and check txv's to ensure properly functioning. Most burnouts occur due to sludging of system oil (ac not engine oil) which deteriorates the coating on wire within the compressor housing which will contaminate refrigerant and oil in the ac system
And make sure not to release refrigerant into atmosphere and gauge amount when recharging to manufacturer specs