There is no known internal problem with your engine, your recoil starter is simply acting up. First, please post the long string of numbers stamped on the cooling air cowl of your Briggs engine (Model, Type and Code). I'm currently guessing the Model is 80202 and the starter looks like this:
[Linked Image]

The internals of that starter look like this:
[Linked Image]

The starter engages and disengages by the use of 5 sprags: inclined planes, with balls that roll up them to jam between the internal and external inclined planes. Over time, sooner or later the central bearing will need to be cleaned and have one drop of oil applied, but unfortunately someone will either put oil in the whole thing, or spray it with WD40, thinking that will help. It won't: the oil will oxidise, forming glue, which will stick the balls in their storage compartment, so they fail to roll up the planes when you pull the rope. When this happens you have to remove and dismantle the starter, clean all traces of oil and glue from its innards, dry it off, put one drop of oil on its spindle, and put it back together. It should then be trouble free for years.

Here are the detailed instructions:
http://recoveryvehicles.tpub.com/TM-5-4240-501-14P/css/TM-5-4240-501-14P_161.htm

At the top of the page you will find Back, Up and Next buttons. 161 is the first page, so you'll need to go forward through the section by using Next repeatedly as you progress. If you have any problems, just ask us.