I have a craftsman snowblower with an electric start. When I try to start it, it just hums for a few seconds then nothing

Try using the pull start if that is an option. You'll be able to find out if the engine is stuck. Your starter is a small electric motor, and it is not spinning. There may be some debris between the electric starter and your engine (could be a small piece of stick or rock... ) that is binding; or it just might have a bad spot in the winding of the starter. You can try giving it a gentle hit on its side. This might free it up. Your snowblower engine might be froze-up (binding) and that's another problem. If banging on it doesn't help, and the engine spins, it could be new electric starter time.

Hi,
Two obvious possibilities; the engine has seized(there are some make-shift cures possible) or there is fluid(gas) above the piston causing hydraulic lock. For the latter, remove the spark plug and carefully ground the plug wire(do not want a fire) and try to spin the engine over. If it sprays fuel out the hole, that was the problem and the inlet needle is not seating. If other, we can try something else.
Peace,
Clarke