Maybe you did not notice that the cooling pumps died.
Many people do not notice due to the "silent" mania of using thermal regulation.

And the power supply is near meltdown, the pressure tubes almost glowing white, expanding massively while evaporating their fission products.
They get looser and looser. When they are started up, you hear them vibrating through the audible range on their way into the ultrasonic spheres.

Better scram now and open the reactor lid after cooldown, to examine the mess inside.
There might be still hope that the reactor does not need to be decommissioned.

coils and capacitors(a bad capacitor) can make a high pitched noise, mine was from the power supply, to help diagnose the source i suggest you to unplug your power supply and with a bent paper clip short the green wire to a black wire on the ATX 20(or 24) pin connector, in the case of an AT PSU you can disconnect all the drives and motherboard and turn it on, if the noise still existing, probably is the PSU.

I agree it's probably the PSU but it could potentially also be the HDD if it's old and bearings are going. Open up the case and put your ear against the inside to try and pinpoint the source. If it is the HDD, it's on its way out and you should image it to another one ASAP.

Yup. If its the PSU, its the same thing like highpitched noise in TVs and monitors.
If there are no other issues, a loose coil can easily be fastened by pouring glue into it. In Germany the brand "Uhu Classic" was popular with TV repairmen. Just soak the HOT and turn the apparatus on, it gets quiet when the heat evaporated the solvent.

I had this problem with an old hard disk.

Alternatively, you may need to perform an exorcism.

Can I use a modern power supply or get an AT power supply with an ATX adapter?

Maybe first find out whether there actually a problem exists.

One of my external drive enclosures' fan screeches very loudly for a moment after power-on, like a woman in a splatter movie just before getting stabbed.
But except for this, all is fine. If tipped, blower runs out smootly for a while with very little resistance. After the initial screech on poweron it just blows fine and strong.

I just respect the blower's individuality, and so I see no need to do anything.

I suspect a fan bearing.

eric1992 wrote:

Can I use a modern power supply or get an AT power supply with an ATX adapter?

before getting a new power supply test with all the hardware disconnected to be sure that it is the power supply the source of the screech.
If your motherboard uses an AT style power connector, go with a modern one, and get one adapter with the -5v and the dummy load, if it is ATX board, then a modern psu would not hurt if you are not using a socket a system with a power hungry CPU.