Sega CD Wire Repair/Replace

I bought a broken Model 2 Sega CD for $10 because it didn't turn on. Replaced the pico fuse, and now it turns on, but it won't read discs. I took it back apart, and the coupler that connects to the 1st connection on the motherboard has a black wire that's been ripped out, too.

Because the wire is fairly small, I don't know how I could easily repair it, and I don't know what the part is actually called, so I don't know what to search for to buy another one. Can someone point me in either of these directions? Thanks!

 

Pictures would help.

 

This isn't a pic of my motherboard, but the circled connection is the one I am talking about. Being that I suck at repairing tiny wires, I'm more interested in replacing the wire than repairing it. The torn wire is the black wire toward the center of this coupler, if that helps.