Dell Optiplex 960's (and other Optiplex models) are normally supposed to run quiet with the fans at low speed, though this can be bypassed in the BIOS with the "Fan Control" setting, which runs them at high speed all the time. The fans can be quite loud at high speed.
Also there are two temperature sensors on the 960 that I am aware of. If the cables to these sensors are disconnected or the sensors are damaged, the Dell hardware will run the fans at high speed as a protective failure mode.
One thermal sensor is on the front of the case and measures intake air temperate for the CPU cooler. The plug for it is near the PCI slot and buzzer. The second sensor is on the power supply, and the plug is near the back of the LAN socket.