I have an 10 year old Husky 61 which for many years has suffered from the same problem. It seems that the pull cord locks up due to too much compression. It will pull once, then lock up and be impossible to pull more than a few inches. Waiting 30 seconds or so usually gets me one more full pull and so on. It takeas about 5 minutes to start it (with swearing part of the routine). It has just been serviced and all appears fine with no problems with the cord, carb or piston and their advice was to pull harder! I don't buy that because sometimes the cord pulls freely.
Looking at various forums it seems that there could be problems with blocked reed valve(s)? Does this seem likely - although it probably should have been checked on the service?
Once running it is fine.
Many help would be gratefully received.