My starter pull rope on my Honda HR 215 broke, I replaced the rope but I can't get the recoil to pull it back! What am I doing wrong?

Hello, I just bout a shredder that has a 5 HP Briggs Model 130202-4015-01 engine, the engine will not start unless its primed, and when primed it will momentarily run unless fuel is manually applied though the carb. I remove, inspected and cleaned the carb and tank, I did find gunk in the tank and the previous owner said he cleaned the tank also (leaves me to believe a lot of gunk was in it) I did notice that the diaphragm appeared pinched at one on the internal vents, but not torn. I did blast air through all the vents on the carb and I did not notice any blockage. I checked the engine without the fuel cap, and used fresh fuel. My initial thought was to order a new carb, but I don't wan to drop $100 bucks to find out it still does not run. Could I be missing something? Thanks for any help that is offered. -Rick-