After finding the part online (about $20 USD, not too bad) I decided I could mess around with the cable - I mean it's broken anyways, right?
So I cut off the part that was broken (all of the exposed part) and stripped away the other half of the end (the cable is stiff at the end, and half of that part is the original exposed part). Plugged that into my computer (with the hacked part monitor-side to make insertion and removal easier in the future) and it works! No high-pitched whining :)