Are you sure the cable is routed under the bottom-bracket? The front-derailleur on the Trek hybrid I have attaches to the cable from above (top-pull). Not being familiar with your bike, it wouldn't hurt to make sure: Look under the bottom-bracket. If you see guides for cables under there, then you can figure it out from there. How does your rear-derailleur's cable attach? Above or below?

I would certainly suggest you get new cable (for both derailleurs) and new housing as well. If you're not familiar with working on bikes - or don't have professional bicycle cable-cutters - it might well be cheaper to have your LBS do the work for you. Perhaps even a full tune-up? Then you could take some time to read up on bike-mechanics and develop a tool-collection.

Good luck!