Deere 15SE mower. Can't pull cord

I have a John Deere 14SE self propelled push mower that is very hard or impossible to pull the cord. I found that if I put a bungee cord on the handle to engage the blade, then I can turn the motor with the pull cord, but it still won't start. That may be a different issue. This mower is gets a port clogged in the carborator that I have to periodically clean. I haven't tried that yet. Anyway, tt started fine the last time we used it. It's fairly clean underneath, so I don't think that is the issue. I'm thinking that there is a brake on the blade that is engaged that is also braking the engine. Does this mean I need a new clutch? I see that there are different parts to the clutch and I might not need the whole clutch. I've also read that in may be difficult to remove the clutch.
Any suggestions?

Thanks