Yes, the derailleur functions perfectly well. When I say I disconnected the cable, I mean that I am now working on the shifter without it being attached to anything, just seeing if it clicks through its entire range. Either way, I know what the problem is now. Basically, when shifting up from gear 8, the clicker pushes on one of the teeth on the round cog which actually tensions the cable. Then, when pressure is release from the clicker, it falls back down to the next tooth on the cog so that it can keep going. In my case, the grease is so thick that the clicker has difficulty falling back down to the next tooth and instead stays on the same one, preventing it from ever shifting more than 4 gears. So it seems like whoever my 'client' took her bike to previously had used the wrong type of grease on the shifters, which brings me to part two of my post.

jimc101: not much to say, but I'd like to clear a couple things up. Do you work in a bike shop or have worked at one? Cause that would explain your belligerence. Let me assure you that I am not trying to pose a threat to bike businesses; I am a 17 year old kid who has been fixing and maintaining his own bike for 4-5 years and as a result, family friends and neighbors occaisonally hire me if they want a cheap tune-up. If I find something which I can't fix (especially if they did not mention it, as it was in this case, since normally I would not take a job I do not think I can do) then I tell them, "I did this, this and this, but found this which you should bring to a professional to fix" that rarely happens because I'm savvy enough to finish 99% of my jobs. And if it does happen, I waive the fee, which isn't a problem because I'm certainly not doing this for the money (20 bucks every other week is a little light), I'm doing it because I am going to go to college with an applied physics major in mind and I love solving mechanical problems. If you were genuinely concerned that I might be doing harm to my customers or myself, you should have told me so in a more appropriate tone, however; the level of bitterness in your posts leads me to believe that such was not your intention.

Thanks everyone for the helpful answers, al1943, your post is what led me to look at what kind of greasing job had been done inside the shifters, so thanks in particular to you.