Beeest upper back exercise out there. Have you tried if you can do one!? It's actually easier than you think.
Try hanging, can you do one? If not, fetch something to stand on. Jump up to the top position, bend your legs and lower yourself towards the ground. Try to go down as slowly as possible. Do a couple of these every time you are at the gym, your body will notice what's going on and you will get stronger really fast, believe me! If you do this seriously I give it a month until you can do your first pullup :) When I work my back I usually do 5 - 6 sets of pullups, where I do as many as I can. Last time I did 7, 7, 8, 7, 6, 4 pullups, for instance.
Past week in exercise:
Tue: gym (chest, triceps, legs posterior, abs)
Wed: gym (shoulders, biceps)
Thu: 3,5 km run + gym (shoulders, abs)
Fri: gym mini (squats + toes to bar)
Sun: gym (back) + 5,2 km run
Tue: gym (chest, triceps, shoulders, abs)