I need to make one thing clear here, it is NOT a humming noise. It is more a digital data noise. If you drag your mouse across the screen or switch windows or do anything related to the display, the sound changes slightly.

It is not an earth loop either. I know enough about this subject to know this as fact.

The dodgy power supply theory is a good one. I also had this problem on my desktop DAW and I isolated the problem being caused by one of the monitor screen power supplies. I removed the earth on that too and it solved the problem. And in this situation I was using a PCI soundcard, not USB, so that discounts it being a USB problem, in my mind.

For me it's not much of a problem because I don't often use my monitor speakers, but I should, some day, find a more suitable solution other than removing the earth connection.

What kind of monitor are you using?

I had to stop using my 60" plasma as it emitted this godawfull digital humming no matter what I tried, much higher pitched than normal hum,

Removed it and went with a 40" LED, humming gone. (And room temp dropped like 20C )

At the moment I am just using my laptop monitor.

Just read the OT properly, you say it goes away when you just run on batteries with the powersupply off, that definitely sounds like a bad switching powersupply.

Has it done this from the start or did it just start to happen recently?

If the latter maybe you could get a new powersupply to see if it's going bad.

I used to have the halogen lighting here run on 12v with a switch mode powersupply and it slowly started doing that digital humming as it got older,  switched to a 120 halogen system of the mains and it went away.

This is why this forum rocks! Thanks all for the replies and things to try,
 
synkotron is correct in the fact that the humming "changes" when I move the mouse.  It definitely stops when I unplug the power cord either from the wall or the laptop.  My workaround has been working from battery (GAH!) when I really need to listen to things. 
 
I'm leaning towards the powersupply in the laptop being somewhat ****ed, but I can't do much about that right now.  I plan on moving to a non-laptop setup at some point, hopefully that will "fix the glitch and work itself out naturally".  (guess the movie!)
 
Anyhow, I may try the HumX to see if it works, it's a cheaper method to try for now.
 
 

Way back I had this Acer TM ( 2004) I paid about $1500 for it which was cheap in those days..  and it had the same issue of static noise via the on board or my Fast Track when on A/C only. I was told to try the ground lift trick and it worked, BUT, My battery died about a month later... Didn't think much about it so I bought a new battery that lasted 2 months??? 
I checked the voltage output and it was actually moving up and down and hard to read???? 

So, beware of crappy power supplies for laptops. 
Now on my shopping list for a laptop is it has to have only a 2 prong AC cord.