How do you know it's a 3-way switch?
1- If it is, try turning the other 3-way associated with it on.
2- Check it again, if the light comes on and you don't hear the same noise, the switch, wire(s) or connection is bad (or just loose).
3- Assuming no, leave the light on, go to the breaker panel and turn off the power to that circuit.
4- Remove the switch cover, and the screws holding the switch in the box.
5- Look for burn marks, charring or loose screws on the switch.
6- If the screws are tight, replace the switch.
8- If the wires are plugged into the back of the switch (round holes in the back of the switch), replace the switch and this time connect the wiring to the screws.
9- Pay attention to where each wire goes so it will work when you replace it.
10- Now you can turn the power to that light back on.
Good Luck! ! !
Retired Electrician - NJ