Are you sure you got the right cable? Is the selector bracket securely fastened to the transmission? If you have a '68 or '69 then you can adjust the cable slightly right at the shifter, but it won't make that big a difference. Is each end of the cable jacket attached securely? I think there's a little U-clip at each end. Why did your cable break? Just old and rusty, or not working smoothly?
Is it an aftermarket shifter? How about the cable? I know my V-matic 2 needs the longer cable and if isnt adjusted just right the ratchet part doesnt work.
What you need to do is have someone go through the gears while you watch the lever. It really sounds like it might be binding. Did you run it the same route? If not it might be bent to tight in some place. Hope this helps. Sean