I can feel your pain! 8 weeks ago I started back in the gym after 5 years (YES years) off. Needless to say I was and still am lifting quite light weights (apart from my legs which have some residual strength from decades of alpine skiing)
Anyway 4 weeks ago I changed my program to a 4 day split program, with the back/bicep day including the good old chin up (reverse
wide grip).
First day ... ZERO! Yay me. My ego took a HUGE beating, and I was in a ****ty mood for 2 days. I knew I had a lot of work to do ... but ZERO was ridiculous!
Anyway... time passes. Now after just 4 weeks of I am doing 3 sets (4 reps, 3 reps, 2-3 reps) which I think is a nice improvement. Still a long way to go... but 7 by the end of 8 weeks sounds like a good goal.
Other exercies I do on back day are lat pulldowns, deadlifts and Db Rows.
Keep at it... dont get too down watching skinny guys do 30 in a row and you will get there.