It sounds like the engine turns over when you try to start it.
I have never stuck my hand on the carb while starting, but fuel goes into the carb and mixes with air, so fuel on your hand is not surprising.
The wires are probably to a sensor for the auto choke, but can't see what you are talking about.
My guess is that your carb is flooding. Try twisting the throttle while you start to clear out extra gas.
More info would help.
Cheers