Have you made a recording with everything unplugged? If you go out in the garden (well, away from anything electrical anyway) and make a recording using the internal microphone and play it back out there too do you *still* get the hum? I'd be surprised if you do.
This is what it sounds like unplugged, though not in a garden away from any other electrical gubbins. (Laptop is heavy, garden non-existent etc.)
Not perfect, but as you can tell, better.
This is it unplugged, using the internal microphone. Not pretty. (The very brief noise at the very start is me, sighing.)
This probably confirms your diagnosis.
Bev.