Is this a High pitched whine or squeal ?
It's probably coming from the power supply.
Does your power switch do anything ? If it does, then it's most likely the power supply.
I'd suspect either
1) your PC power supply is not working
2) you motherboard/NIC is broken.
If you're confident to open your PC, Unplug it from the power lead, Open your PC and unplug the power supply from everything.
(motherboard, drives etc)
then plug the mains power lead back into the power supply. If the noise is there, it's definitely your PC power supply whining.
If you have or can borrow a voltmeter/multimeter, measure the voltage on a power supply to hard drive connector. ( The old ones are easier than SATA ones to use for this). Voltages are DC, up to 20 volts. The voltages present normally are not dangerous, but take care not to short the power output leads together. As your fans and HDD's spin up, the voltages must be almost right.
From the RED to black wire(s) there should be 5.0Volts. Tolerance is around +/- 5% so max 5.25 min 4.75
From the Yellow to black wires there should be 12.0 volts. As low as 11.5 volts in fairly normal. Over 12.5 is abnormal.
The connector to the motherboard carries other voltages, but testing 5.0 and 12.0 is a very important (easy) first start.
The measured Voltage pulsing up and down is bad. Steady voltages are good.
The ORANGE wires on the motherboard connector carry 3.3Volts : they are critical.
If the power supply looks okay, it may be the motherboard. If you've got a spare (old) computer or know someone with a spare junk PC, you might try swapping your power supply into the junk PC. If the junk PC boots, then it's probably your motherboard, if it doesn't it's probably your power supply. If the power supply has wrecked a junk PC (which seems unlikely, given your drives and fans run okay), well, that's not too bad.
Beyond this it is time for someone with a background in computer repair.
The hissing sound is normally the power supply being overloaded. The standby power supply is hissing ( when the PC is off).
The most likely reason is that the large (electrolytic) capacitors inside the power supply have dried up and are not storing enough power as the mains voltages oscillates ( it's alternating current), so the power supply struggles and the transformer coils ring ( that hissing sound). Poorly varnished or loosely wound transformers will hiss from new, when not overloaded. Old TVs get this way for similar reasons.