I have a craftsman 536.884331 snow blower it will start and stay running as long as I hold the electric start button if I let the button go it dies it also will not start with the pull start

 

The starter motor is spinning all the time you hold the START button in. This can ruin the starter motor or flywheel or both. Count your blessings. My guess is you have a key switch for operating your machine. It has 3 positions, OFF-RUN-START. Normally, when you turn the key from START to RUN, it removes voltage from the starter and continues to provide voltage to loads such as electric fuel pumps, lights, etc. When the key is in the OFF position, voltage to all loads are removed and the wire to the ignition module is grounded which stops the engine. I think your switch is defective by grounding the ignition module in the RUN position. Use an ohmmeter to check if the wire to the ignition module is grounded in the RUN position. If this is the problem, replace the switch.