What I would first start to look for:
Check for DC at the wall outlet. Check if the transformer cover can be moved by hand, if so then look at the bolts holding down the cover. Remove the cover and see if the rubber or elastomer bushing is still intact.
That is a 60hz buzz so it’s an AC issue, and it’s either the transformer or the soft start relay coil (those are the only two ac inductors I can think of). If it’s the transformer, then it’s probably the bridge rectifier has an open diode and only 60 hz is getting to the secondary instead of 120hz. If it’s the relay, then its probably a shorted rectifier diode, sending ac instead of dc to the coil and causing the contacts to chatter.