Sometimes people will refer to the case and all internal parts as the CPU. I have folks coming to me at work all the time and say "my CPU is rattling can you fix it" well a CPU can't rattle, a case panel/fan/loose drive can.
In all my years around computers I have never heard a CPU make a sound, well outside of a thump when I dropped one.
The hum will always be some other part of the system. I have power supplies that will have a hum/whine to them as they are dieing, but this is a very noticeable and annoying sound.
To jump start the PSU to see if this is your noise. First unplug all power connectors and from the wall. Then on the main 20/24 pin connector find the green wire (there is only one) shove one side of a paper clip into the pin for the green wire and the other side to any black wire. Plug it back into the wall, if your PSU is the prob you should still hear the whine.
If no noise, unplug from wall reconnect the to the motherboard, remove the video card, power up the system. If you hear the whine its the motherboard, if you don't hear it, the video card is the issue.