When my goal was Just One Pullup, I did slow curls with a 5 pound weight, while I watched tv. I rested the muscle for as long or longer than I used it for each curl.
After a few weeks, I decided to see if I could do Just One Pullup, and was surprised to find I could do 10.

I have never been able to do even one pullup. After climbing weekly for year and a half, I still can't do even one pullup. Not that I've been aiming for that as a goal, but still.

Good luck.

Working up to pullups is tricky, because it can be hard to properly exercise those muscles at a lower level. The gym I go to (BSC in central square) has a neat machine for doing assisted pull-ups, which counterbalance your weight as much as necessary. I can still only do about four full pullups, but I can do three full sets of pullups at my weight minus thirty pounds - which is a definite improvement from when I started.

When I was going to that gym (before breaking my arm), my experience was essentially the same. Having just a little assist is often enough to be able to pull up. If you have access to such a machine, give it a try.

Also, proper technique can help a lot. The starting position is generally with the upper arms horizontal; starting from a hanging position is much more difficult. Keeping the shoulders down and the elbows right at the sides (not flared out) will help use the larger muscles instead of only the biceps.

I, for one, think it's great that you have such goals, that you're working toward them, and that you are willing to tell other people about them.

You are way ahead of me. And even if you weren't, you would still rock for doing those things. :)