Here are a couple of diagrams of how some 3-way switches that I have seen were wired. Take a look at the available wires and see if you think they can be wired to work properly. In both diagrams, each 3-way switch basically has a hot, a neutral and one single wire going up to the light fixture. 3-Way Switch Diagram 1: 
In the above diagram I ran up on this situation one time on a service call for a 3-way that wasn't working right. I have to admit that upon first looking at it I had to scratch my head for a few minutes before I was able to get it working right. This next diagram was how one was wired that I ran up on that did work and it made me wonder how it could possibly work right. After seeing how they had it wired it made sense then. 3-Way Switch Diagram 2: 
I have seen 3-way switches wired about every way possible but these two had to be tops in the unusual department. To see the answers or solutions on how to wire these to make them work just click here. *
