I just finished upgrading my Dell Optiplex 780 to Windows 7 64-bit. The tower was producing a very irritating high-pitched noise after this upgrade. After a bit of searching, I found this discussion that seemed to match my problem:
http://en.community.dell.com/support-forums/desktop/f/3514/p/19292677/19546282.aspx
I tested the BIOS setting change for C State Control suggested by carl.hobbs and petewitt. It solved the problem instantly.