There will be loud buzzing coming from the computer from inside the tower. If it has been failed for long, the chassis may be warm to the touch.
To Resolve: Edit
1. Find out where the sound of the fan is coming from. It could be the CPU fan, the PSU fan, or some other fan, try and pin-point the location.
2. Run Diagnostics (F12 on startup). Many times it will come back with no errors found, that's okay - it just means it hasn't been ineffective long enough to effect the internal components.
3. Get the service tag/ serial number of the computer and call the manufacturer. They will replace fans for being annoying, even if everything else works. If the computer is not under warranty, you will have to open the computer up and try and fix the fan yourself. Many times taking the fan out and placing it back in place will resolve the issue, along with a good air spray.