[with power fully off] and then be sure to touch any part of the internal metal immediately and frequently to be sure to get rid of any ESD. Then turn the system on. It will then be a simple matter to locate the offending source. There are no voltages inside that can zap you.
You can touch the hub of the fan to see if that causes the vibration to cease or change. You can touch the hard drive sides with no potential to damage it.
My searches here seem to indicate this low constant hum is not the hard drive but a fan. It is a noise I usually hear when I power up but disappears as the computer "warms up". Today, however, the hum did not go away. Although the back grille is slightly warm, I think that is the usual. When I put my hands on the sides of the box I feel a vibration, which I don't think was there before......vibration is stronger on one side than the other.
Other than using the compressed cold air to clean out the dust, I do not know my way around inside the box.
Does this sound like a fan or hard drive?