I don't know what the buzzing is, but I would be more likely to guess that it is the heating unit. You can test that by taking the wafer out completely. With no wafer to click the switch to turn off the heat, it should run and run and run until you unplug it.
To test the wafer, put it in and run the incubator to set the temperature. If it varies too much, then you could replace the wafer.
It might have been used only a few times, but if it's too old than it's too old... The solder eventually cracks and the ether inside leaks out. It will still seem like it's working, but an old wafer will not react as quickly to temp changes, so the temp will range too widely.
I had this trouble the first time I tried incubating last spring. I got an incubator from a guy who had it up in his garage a bunch of years, and he got it from a guy who had it up in *his* garage a bunch of years. I didn't know about the wafer getting old, and the temp went up to 107 a couple times and cooked most of my eggs.