Thanks for the advice guys, really helped me out here. Hopefully the paste will do wonders for few months, I didn't particularly fancy shipping the PC as I've already spend a ton these last few weeks! :p

So, it's still bugging out.

I have now done the following:
Dusted the fans, including the CPU fan.
Dusted the ram sticks and reattached them.
Reapplied thermal paste on the CPU
Changed power outlet
Moved it on top of the desk, closer to an open window
Turned an extra fan on in the room to cool the room temperature down.
Made sure all the fans are operating.
Checked the wires were plugged in properly.

I think it's now officially outside my jurisdiction and I should send it for repair & bitch and moan about how shitty the tech support I've received as well as the fact that the rig has failed within two months of purchase.