Strange sound coming out of computer tower?

I think that one of your fans is likely dead. When a fan dies it either just stops, or it goes for a second quickly, then abruptly stops. This is an easy fix if your fan is dead.. you just need to go to a computer hardware store and get an appropriate case fan for $10. Open up the side panel while the computer is on (do not touch anything inside) and observer the fans to see which one is doing it. If it is the fan on your CPU heat sink you should turn off your computer and get a new fan for it immediately.