A relay that buzzes is not being fed enough juice to keep the relay contacts closed. The contacts close, the voltage available drops, the coil opens due to lower volts, the voltage recovers as the 'load' is gone, the coil closes again, the volts drop as the load is re-applied, rinse repeat... Bzzzzzzzzzt.
Your voltage is lacking, or your current capacity is down. The ignition switch could be faulty, the grounds on the relay bad(though they are mostly grounded by computer if computer controlled, so it would be battery voltage not ground)
What is your battery state of charge? Resting voltage?
tom