How can I attach a replacement pull cord on a Murray push mower?

I think you have to replace the whole black round steel cartridge that the cord wraps itself around, and it's about 23 bucks.
Three screws to remove.

Tecumseh or briggs? Either way its cheaper to do yourself, usually you take the shroud off, and either bend the tabs or remove the retainer holding the recoil pulley in, and pull it out (it'll unspring the spring) and put the cord on (burn the ends to a point helps) and wrap it around and tape it on at the end, rewind the coil and put it back in, carefully hook the coil to the pulley, and put the retainer or tabs back down, and pull the rope out and tie it in the handle.

Remove the blower housing, then the old rope. You will need approx. 7 to 7 1/2 feet if the pull handle is on the handle bar. Then rewind the spring with the entire blower housing intact, hold the pulley firmly, insert one end of rope, and tie a knot in the end after it is through the blower housing and pulley. Tie another knot in the other end, release the rope, it should pull the rope into the housing.