OK a quick update...

• Not the UPS - bypassed, off and unplugged to test
• Not a mobile phone, nor any other wireless devices - turned the lot off and unplugged to check
• The noise audio changes when using the PC sound card, but still there
• Internet disconnected - no change 
• No monitors connected - just headphones - no change
• I live in the country with no-one nearer than 50 metres
• Mouse and keyboard are corded
• Paul P - don't worry, I made up a mains in-line socket box with an external switch to lift the earth individually on each mains powered piece of kit. So far no success though.
• No everything is balanced, but a DI box is on its way!!
• At the moment, there are no audio input sources or phantom power connections
• Important - A WINDOWS UPDATE BERWEEN 27 DEC AND 2 JAN CAUSED ALL MY VSTs TO STOP DELIVERING ANY OUTPUT. NEEDED A RESTORE TO CORRECT THAT - THANKS MICROSOFT!!

Disable sound in Windows and see what happens.

(I am assuming your monitors/headphones are connected to you audio interface directly.)

Tremor
Paul P - don't worry, I made up a mains in-line socket box with an external switch to lift the earth individually on each

I don't have a problem with your lifting the ground temporarily (while not touching the case of the equipment) to see what happens, but my concern was that if it did fix your problem that it would then be left that way.  If there was a ground loop (which isn't the case here apparently) it can be solved in better, safer ways than lifting the ground on the power cord.  And since there's never a reason to not use the ground, there really isn't much point in playing around with lifting it.  Better to lift the ground on a cable.
 
 

The OS itself has nothing to do with the noise issue.
 
The problem is almost surely ground related.
A poor quality USB cable can induce noise (which sounds like "digital hash").
 
First, make sure your studio is powered via a single outlet.
Make sure to use balanced connections with decent quality balanced cables.
 
I'd start with nothing but the PC connected to your (audio) monitor setup.
Disconnect literally every component that's not absolutely necessary for the PC to run.
You need to establish a base-line "clean" signal... and build (add items one-at-a-time) from there.
 

Do you have an onboard sound card that is enabled (even if you aren't actively using it)?  The shielding on these things internally is pretty terrible.  I get all sorts of noise coming across mine that drives me crazy until I completely remove it from the chain.
 
As an IT support pro, I can tell you that I've seen MANY times where moving a mouse makes noise that shows up in the audio spectrum somewhere and it's usually attributable in some way to a cheap built-in soundcard.
 
See if you can disable this in the BIOS on the system board and see if the issue goes away.  Of course, you might actually want this sound card, but maybe this will help at least troubleshoot it. 

Tremor
OK a quick update...

• The noise audio changes when using the PC sound card, but still there

I think everyone is picking up on the same thing here... and seeing your last bullet point, the below may "have to wait" but will throw it out for when the time comes.
 
If you go into "Change sound card settings" in Win7 with the audio interface online, are all "Realtek" devices disabled? You can right click that list to "Show Disabled Devices." This is definitely worth checking (but may already be done).
 
It seems you have already checked all hardware outside the box. Any other chords/cables to external hardware not taken from the loop yet (quick double-check to what Jim said above)?
 
Iobit's Advanced System Care (free version) is a nice utility to check numerous things on the machine. You can let that run itself, see what it finds, and go from there.
 
***Below is more of a "last resort," although is also good housekeeping when done properly*** 
Assuming this is potentially hardware internal to the box, it is driven by "something." In a situation that you are actively monitoring your machine, you can run Windows Task Manager and begin on the "Processes" tab and begin right-clicking processes and "End Process Tree" on things. Some are fairly self-descriptive, and you will eventually kill a main Win7 process and shut your system down if you exhaust this list (so do not do this while doing anything else). You may find a process using a piece of hardware that is unnecessary/conflicting on your machine. If you do happen to find something like this, the next stop is to disable it during boot in msconfig.exe (see below).
 
I have a truckload of programs/utilities disabled during boot in "msconfig.exe" (both the "Services" and "Startup" tabs), and when I discover more or these via the above this is where to disable them from auto-loading on boot. They can still be launched manually, but sadly... some which are manually loaded need to be disabled again this way, since they immediately add another registry entry for startup (Adobe being a prime offender of this).

Tremor
To clear up a few suggestions. It's not residual demo white noise, it's too low level for that although the noise does have a "white noise" sound to it.
The noise bursts are "regular" i.e.about 2 seconds apart and each lasts for about 500mS which would seem to indicate that they are being "clocked" somehow - the PC perhaps?

(The forum software preview just nuked my wonderful post.)
 
Do you hear a single beep when the computer boots?
this could be a beep code:  1 beep  dram refresh failure
Seems the computer would not boot. But, a client of mine had some intolerant ram added to some of his machines. The computers booted and worked for hours. But when the ram was accessed the computer would start acting inappropriately.
 
Test with only 1 ram chip at a time.
 
next:
Connect headphones to the on-board sound spkr/headphone jack.
Boot to BIOS. Hear the noise?
Yes/no: whilst there:
Prolly done this: disable cool and quiet, set fan to full, disable network card, serial port, parallel port in BIOS.
If you heard the noise reboot to bios. Hear it now?
 
If not: boot to windows safe mode. Hear it?
If so, we know it is something basic.
If not, boot to regular mode. Hear it?
If not, enable the network card. Hear it?
 
On-board video available? Remove the vid card.
Disconnect the dvd and non-OS disks.
 
Windows:
  services.msc
  disable network services, shadow service, media play sharing service,...
  Task scheduler
    disable all phone home items
     user experience
 
   disable all non-useful items
     defrag
      disk/pc health
 
disable any startup items that phone home: java, adobe,..
  disable any blue-toot, and keyboard/mouse special software
 
And so on.
 
Did Aria PC include the standard 5-pound computer hammer?
 
 

Update..
 
Using only PC with its soundcard (saffire disconnected) and headphones - no noise ! Full volume on Youtube mp3 is silent apart from the track. That would seem to discount start-up items.
 
X3 doesn't see the sound card as an output device for some reason - not a listed device, so unable to output audio to it - strange.
 
next task is to remove the saffire completely from my rack system and connect it directly to the DAW with a short firewire cable and the same mains connection as the DAW.
 
Another slight problem has also arisen. When using the VSTs I occasionally get a short load burst loud of the VST I'm playing at the time.
 
My sanity is coming into question as well as ruining my music as I can't concentrate on anything other than the noise problems.
 
Aria did not supply a 5-pound computer hammer, but I'm getting close to needing one!!!!!

I had the same issue for months. My dad and I did some troubleshooting just as you have been recommended. In the end it came down to poor grounding in my power lines in the house electronics. I fixed this by buying a power conditioner for my gear. I ran everything through the power conditioner: PC, monitors, drum machines, keyboards, etc...

This ended up being the solution to my problem. You may want to consider this option?

DSProductionz
I had the same issue for months.

This was a repetitive noise as described by the OP?  
 
For me it was random static.