It is possible that you have 2 different issues. It is hard to tell from your description if you are saying that the wind down noise is the noise of the starter running and if it is, is it running w/o the key switch activated. Solenoids are the most likely cause for allowing the starter to run on- but not the only one. They are not typically a fuse blower- but could be. On a 4 post solenoid one of the 2 small wires supplies a ground and the other 12 volts when the key switch is activated. If I am assuming something I shouldn't, please elaborate on what you believe the noise is.

I don't know it you model has fuel pump or not. IF not the tank should be higher than the engine? Well, Not that uncommon when mower sets. This is what I would Do> remove the gas line front the tank up to the fuel filter lower it gas should poor out. If not you have and obstruction in the tank or hose. Now that you got gas up to the fuel filter. remove the hose after the fuel pump (If you have one?) if not gas goes directly to the carb. and gravity feed supplys fuel to the needl and seat in the carb. bowl) With fuel pump hose remove at the carb. crank the engine over catching any fuel in can that might be pumping out. Fuel coming out? attch hose to carb. Now you can PRIME the engine for starting. I never attempt to start an engine that's being setting without priming it. (to do full prime remove the spark plug or plugs. connect and crank engine to see if you have good spark. GOt spark, then using carb. cleaner spray 3 to 4 second blast of carb. cleaner down spark plug hole. Crank then engine over (outside with spark plug wire away from spark plug hole so it won't ground out and light the carb. cleaner) Crank the engine for 3 or 4 seconds to blow out excess carb. cleaner that hasn't evaporated. Put the spark plugs back in, remove the air cleaner and spray carb. cleaner down the carb. venturi (opening) one to two seconds. Now you have the engine primed to start and it should fire within 5 seconds. If not repeat spraying carb. cleaner down the carb. Now that you got it firing off the carb. cleaner and it dies (make take two or three times for it to take off on gas due to air trapped in the fuel system. If that fails then I would remove the carb. bowl and spray the needle and seat.. This works on any gasoline engine and I have rarely failed to get any gas engine started reguardless how long it set. Basic as suggested you have to get fuel to the carb. before you have chance to get it started by priming it. If it don't run off gas just priming fluid then you have to figure out why gas won't got through the carb. and run on it's own. which as suggested needle stuck to the seat or the jet passages are plugged up.

If the battery is more than 3 years old--buy a new one! Then, clean up all of the connections, such as ends of battery cables, and especially the ground wire where it bolts to ground, i.e.tractor frame, or body of tractor. Use new bolts, nuts, and lock washers to connect the new battery! This will make sure you have a good electrical connection in the starting circuit! there is also, usually, a fuse in the line somewhere. It will be one of those new style flat fuses, and easy to find. See if it has blown. You'll be able to tell easily. The little curved piece of metal in it should look to be in one piece. If it has blown, there will be a gap in it, and a burnt look. Also, the bolted connections to the starter solenoid are known to get corroded and cut off current to the starter solenoid! And, any battery cables with a green powder coming out of the covering are ripe for replacement. The seat switch wires should be connected, to avoid hurting anybody who might manage to tamper with the mower if you aren't on it! Especially little kids!

If you have a pair of jumper cables, try starting it with the cables connected to your personal vehicle. You could also (and carefully), take the positive side of the cable then touch the connection on the starter motor of the mower. See if you can get the starter to engage. You might try removing the spark plug(s), then again hit the starter motor to see if the motor is free. I'd jump it myself with a large 12v battery off my car. I happen to have a large battery charger that can produce (or so it alleges) 225amp starting power. Which is used to start dead batteries on cars. Your ignition switch might of gone south (easy to replace), make sure your safety switches all are working--so the starter will receive power when you hit the start key. 120 is way high.