Thanks,
Dave
If the hum goes away with all breakers tripped off, restore the breakers one at a time, checking with the radio for hum with each breaker reset. Eventually you will find the circuit which is feeding the hum generator.
I recently had a problem like this suddenly occur and suspected that the control pot on one of my SCR lamp dimmers was going bad. As it turned out, it was a cheap Chinese blowdryer bought by my wife - the thing generated RFI whenever it was plugged in, even turned off!
Most common household RFI sources are (1) SCR dimmers; and (2) desktop computer power supplies. There is no cure for SCR dimmer noise aside from replacing them with plain switches; a RFI filter is effective for computers but it must be installed right where the computer plugs into the wall outlet.