If it just "died" then the ignition quit or the fuel stopped flowing.
Throwing parts at it is not the best approach. The valves may be OK, I can't see them from here, but they wouldn't have caused a sudden dying.
Put it back together and check for spark, use an old plug with the gap opened a bit more and watch for spark as you pull the rope. If you have spark and the thing doesn't fire, remove the spark plug and put a few drops of gas down the hole and quickly reinstall the plug and pull. If it fires briefly, then you have a carburetor or fuel pump issue, and that is where I would have started.
