That sounds suspiciously like a prefab system on which the case was designed around the existing motherboard.
Most USB hookups have multi pin jacks that can only be plugged in one way - so that even a newbie can't really make a mistake.
The mainboard manual should tell all.
Here's something for you to consider though. Many USB ports in computer cases are only USB version 1.0 compliant and NOT USB version 2.0 - which means that those ports would not be able to run many if not most of the newer digital cameras, scanners, external USB hard drives, external USB CD/DV rom drives, and more.
Your best solution would actually be to simply IGNORE the wires and those two USB ports, while installing a Quad USB 2.0 PCI card with 4 new and compliant USB ports.
What's REALLY confusing about your post, is that SINGLE wires or wire strands, are normally strictly for hooking up the hard disk, power, reset, and other LED lights or contacts on the mainboard. I have NEVER seen a single or double strand of wires for USB hookups, except on computers, as mentioned above, where the prefab system was designed with both the case and board in mind, to begin with.
The quad USB PCI card would really be your best solution, and you can get those online for $20 to $25 bucks. Check with Ebay.
Hey Intel, AMD rulez!