[Build Help] Flickering graphics when transferring files

So, I've put my build together over the last few days and everything seems to be running quite nicely except for one issue which I'm not sure how to deal with.

When I'm transferring files from one drive to another, my monitor will start flickering. When the transfer is completed the flickering will stop. I can live with this but I'm afraid this could be a symptom of a larger problem. I am inexperienced so I haven't even heard about this issue and Google seems to be suggesting it has happened to others but there isn't much info out there. I'm not sure if this could damage my computer if I don't address it. I just don't know what to do. I'd appreciate any input. I'll include a list of some of the things I've tried already below / information.

My build at present:

Coolermaster Silent Pro 700W PSU

XFX Dual Fan 6870 GPU (just one)

i5-2500k

1xAgility 3 120GB SSD

3x 2TB Samsung Ecogreens

1x 900GB Barracuda

1x 700GB drive

BenQ BL2400PU 24'' monitor

2x4 Ripjaws

Gigabyte Z68A-UD3H-B3 Motherboard

Hyper 212 fan

Fractal Design Define R3 Case

Notes:

• I've tried removing 3 of the drives and it made no difference.
• I also tried making sure the monitor was plugged into a different outlet entirely.
• As of right now, the monitor is connected to the GPU using a vga cable running through a VGA to Miniport adaptor - however I'm not sure this is the issue given that it's happening only when the computer is under load but nonetheless I'm getting a DVI-D later today so I'll be testing that.
• The drives seem to be transferring at full speed and I cannot see any issues with anything other than the fact the screen flickers during hard drive load
• No flickering seems to occur when running a lot of programs, downloading from the internet and playing Starcraft 2 at the same time
• I have updated to the latest GPU drivers / machine is fully updated
• Even under load I have not seen any temperatures of anything go very high at all
• I ran the build through a PSU calculator prior to purchase and it seemed to suggest that a 700W PSU would cover my needs under load and leave me with a 20% margin of error - could this be wrong and the source of the problem?
• I notice that when I scroll down the monitor will fill white text with yellow during the scroll - this happened when I used a different XFX 6870 that I have since exchanged. I haven't found a solution to this and I don't even know what it means.
• I'm thinking about maybe upgrading to a CM Silent Pro 850W instead as a solution but I thought I'd ask you all beforehand just in case anybody had experience with such an issue - I'm also thinking of just living with it so long as it won't damage anything or it's a sign of something worse. I don't intend to do much transferring beyond initially filling up the drives.

I'm heading off to work right now so I'll be back a little later. I hope I've covered enough bases to be helpful.