I am noticing a faint squeaking sound coming from the lower back part of my desktop.  It is rhythmic, but not 100% consistent.  About one squeak every half second.

I don't know how long it's been going on.  I noticed it today because I heard the same sound on my studio monitors which I was testing out for the first time in months.  I then cranked up my headphones and heard the same sound.  In the process of testing the speakers and headphones I noticed that the same sound was coming from the lower back of the computer itself.  

So, the same rhythmic squeaking sound is coming from:

1) lower rear of computer
2) studio monitors (plugged into Delta-44)
3) headphones (plugged into Delta-44)

I have a second sound card (Xonar) but no matter how much I turn it up, I cannot hear any squeaking on it.  So, it seems that only the Delta-44 is carrying the squeaks to its headphones/speakers.

Changing the input and output volume sliders in the Delta-44's Control Panel has no effect on the loudness of the squeaks coming from the speakers (or headphones).  In order to make the squeaks quieter, I have to turn the volume knobs down on the speakers (or headphones) themselves.  Of course, changing the speaker/headphone volume has no effect on the loudness of the squeaks coming from the computer itself.

So. the squeaking seems to originate in the lower back of my computer, and then get transmitted to the Delta-44 (but not the other sound card).  The two main devices in the lower back part of the computer are the power supply (it's bottom-mounted) and the video card.  I opened up the case but couldn't figure out which was the culprit: it could be either the power supply or the video card, or some other part of the motherboard.

Given the symptoms, which do you think is creating the noise?

a) power supply
b) video card
c) something else?

You will most likely have to open the case to try and find where its coming from. 

As I stated in my first post, I already opened the case and listened, but couldn't pinpoint the source.  My ears aren't that good!  I even rolled up a piece of paper to use as a makeshift stethoscope but still couldn't tell where the high-pitched sounds were coming from, other than they were loudest when my ear was near the lower back of the case.

Using something like a stiff piece of cardboard you can momentarily stop the fans on both the video card and power supply.  That should identify or rule out them out as the squeaker.

A few years ago I got lazy and instead of building my own PC, I got a premade box, it used to suffer from audio noise as well, turned out to be one of those wires used to connect to extra external ports of my pc case from my motherboard was passing to close to some component that was creating a 'pulse' noise, or vica versa, cannot remember which, but simply relocating an internal cable/wire by a few cm resolved my problem.
I cant remember if it was for USB or audio jacks, too long ago.

c) mouse

I'm pretty sure the squeaking sound isn't a fan, or anything rubbing on something else.  It seems to be more like what some people call "coil whine". (It sounds "digital" to me, if that makes any sense)
 
I'm wondering if the problem is related to the fact that my Delta-44 is connected to an OMNI I/O breakout box, which runs on US power, for which I have a transformer (I live in New Zealand).  I suppose I could disconnect the breakout box and see if the squeaking goes away.  Next time I have a chance I'll try that.
 
I know that video cards are often notorious for making strange noises.
 
Do power supplies ever squeak?

Fans in power supplies can make a squeaking type of noise, which is not good, is usually accompanied by a vibrating type noise as the fan becomes unbalanced, as it indicates that the fans bearings are worn out or caked with dirt, which results in the fan not working adequately or at all, resulting in an overheating problem which results in your computer not working.
Its easy to tell, its usually the sort of noise you hear from the other side of the room, and is more constant like a drone, that cuts in and out when it feels like it, before eventually becoming constant, before the the power supply literally fries itself.

I found some videos which have sounds similar to what I am hearing:
 
https://www.youtube.com/watch?v=UPU9ENJQSU8
https://www.youtube.com/watch?v=3HFjeUbKVNc
 
In those videos, the noises are coming from a power supply.  What was interesting is that when I searched for videos on "psu chirp" or "power supply squeaking" etc. I kept seeing the brand Corsair mentioned (more than any other brand).  My PSU is a Corsair.  So at this point I'm suspecting the PSU to be the culprit.
 
I'm not sure if I should order another PSU, and if I do, should I get another Corsair like mine (so I know it has the right connections), or a different brand of PSU (so there's less chance of noise)?
 
If I go for a different brand, any recommendations on one that is nice and quiet for Sonar?  My current one is 850W so I wouldn't want to go less than that.

850W is rather overkill unless you plan to use the PS to fry things on too. I cannot see sigs from a phone, but I highly doubt that is required (or desired) for your machine.