As soon as even the tip of the external hdd plug touched the usb port, my computer will completly, instantly, freeze. If the plug just brushes against the back of the computer case my computer will freeze for a few seconds...
This external hdd works perfectly fine with my laptop though, and has previously worked with this computer..
(i'm not yet willing to try a system restore when it seems like a hardware issue)
OK, can you try the HDD in a different desktop computer? Sounds like the drive has some kind of issue with grounding the shield on the USB cable – if it was the computer being that sensitive, it would probably (but not necessarily) have had issues when you touched the port.
Try plugging the USB cable into the computer before plugging it into the drive – if that is possible. Also, try plugging the computer into a different power outlet, preferably in a different part of the house. But the most likely solution will be to replace the power adapter for the drive – try a different adapter if possible (make sure it has the same output ratings and polarity).