Bicycle Tutor

Hello,
I recently acquired an old mountain bike. I am no bike expert so I know very little terminology, but I am trying to fix it up. I spent the day working on it and now it is ridable, however I realized that the rear shifter seems broken. The front gear shifter works great, but when I try to change 7-speed gear, nothing happens.
In particular, when I try to change the rear gear, I do not feel any "tug" on the wire that goes to the rear derailleur. I am led to believe that the problem is somewhere with the wire. I have adjusted the wire to be tight, but I still do not feel any tug from the shifter.
Is there anyway to diagnose the problem further, or even better, fix such a thing?
If it matters, the shifter seems to be a Shimano 200 GS. It appears they do not sell these anymore, so buying new ones seems out of the question.
Thanks for your reply!

I should have mention as well -- when I pull the lever to change gears, there is no resistance. The lever just slides. In comparison to the front shifter, there is some friction that forces me to push a little bit harder.

Initially it sounds like the cable is broken.
If you can pull the inner wire from some where on the frame then it may pull out. completely.
See Park website (Shimano STI) may help:
http://www.parktool.com/repair/readhowto.asp?id=117