The hamster which powers your PSU may be ill or dying.
"Whines" are often attributed to coil noise ... PSUs and GPUs being the biggest culprits. When you say people on communication software could hear it, do you mean it was feeding back directly through your headset? Or do you mean it was loud enough to be picked up by the the mic? The first situation might suggest a grounding problem with your new case. The second I'd say is more likely the new GPU.
The sound was feeding back through my headset, they said it was like somebody whistling softly 20 ft away.