I have a coil saturation tester, when I increase the current to much the coil saturates and start whining.
http://www.pa4tim.nl/?p=1859 for more info
The core of an inductor is a self inductance "multiplier" the amount is stated as AL.
If the current through an inductor with some core gets to high the core looses his function (the magnetic field becomes to high), the AL drops and the selfinduction too. This results in more current that cause even less self-induction etc until something dies.
An thing that can happen is movement of parts producing soundwaves. I had a Murphy receiver that had an audio transformer who thought he was a loudspeaker. And rather loud too.
And smps frequencies can drop into the audio frequencies but we can not hear audio frequencies in the form of EM fields, something must turn them in to audio waves first ("air pressure" variations, like a speaker does) That can be an transformer/inductor and maybe some types of capacitors can do this too. But as far as I know they drop so low only around idle, not under full load.
If the computer works fine then I think something is resonating/vibrating and so produces audio. If it saturates the videocard runs out of juice and I think that will be visible or noticeable. If you can reach it you can find the part using a piece of tubing as a sort of stethoscope. I made one using an Y splitter and the rubbers from those in-ear-headphones. I made that a while back to find the cause of a ticking sound in a calibrator, turned out to be a cap that was breaking down under certain conditions.
If you have the space you can also use a screwdriver. The handpiece to your ear, the tip on the component. I used that while working on motorbikes and cars to listen to bearings.