-nohing -would stop the engine... (not even) THE KILL SWITCH.
Fix that first!
Do you have an OHM meter or 'Continuity Tester' ?
You can get a multi-meter at Harbor Freight or Radio Shack for $5.
This a cheap tool with many uses so get one ;-}
Set it to the 2K-20K ohm scale and hook up the leads to your kill button wires.
When you push the kill button it should pretty much zero out meaning the button works.
If not you should get some other button to use.
If it does, and you hooked it up like the kit indicates, one wire to the motors white wire and the other to the frame, put your probes between the wire you hooked to the frame and your spark plugs screw or any motor bolt. If it doesn't zero out then your motor is not grounded to the frame.
You can either tie the frame ground kill button wire to the motors black wire, hook it directly to a motor cover bolt, or ground your motor to the frame.
Check for a stuck throttle cable.
Make sure the slide in the carb comes all the way down (remove the air cleaner to see that).
If you didn't take the slack out of the throttle cable with the cable adjusters on the throttle itself and the top of crab, what tends to happen when you give it throttle and then lay off it the outer cable shield will tend to pop out of the top of the carb hole and hang up on the top of it thus acting the same as turning the throttle.
The inner carb slide can get hung up for no apparent reason too.
I have a brand new carb that does that on the bench now and can't see why, but as wheelbender said, take off the air cleaner and work your throttle from off to full and back
slowly and verify it always goes all the way back down.
If not then are a few things you can for that but lets narrow the problem before tackling the help for what it is ;-}