You should pull the head off to see how bad it rusted up so you don't waste your time. If it is only lightly rusted clean up what you can and put the head back on and fill the cylinder with penetrating oil or Marvel Mystery Oil and let it sit for a few days then work the crank back and forth until it breaks loose.
If the water gets into the cylinder head, it could create rust on the valves, cylinder liner(s), piston(s) and piston rings, causing the engine to "lock up".
Is it an OHV engine? If so they would be loctaed above the piston head on your mower.
There is too much oil in the crankcaseWorn out valve guidesWorn out piston ringsBlocked engine breather
Worn piston rings. Incorrect weight engine oil. Gasoline mixed with engine oil. Crankcase overfilled with engine oil.
Could be several things or a combination, most requiring an overhaul or replacement of engine. Piston rings are shot, piston shot, valves burnt, broken or bent.
There are 2 long "wires" with springs on them attached to the carburetor. One goes to the governor which looks like a small lever that comes out of the engine. If you are thinking of disconnecting it to make the mower run faster - DON'T DO IT!! You will be risking a blown piston rod and lots of internal damage to the engine.
bad piston rings
It means the engine has been fed too much gas. If you depress the gas pedal on a car or truck many times before you start it, the same thing will happen. A gas engine, whether it is a small lawn mower engine or a truck's engine works the same. It needs a certain ratio of gas and air in order to create the explosion in the piston chamber that makes the engine work.
You either have a bad float or/and bad needle and seat, which is causing the carburetor to flood. The fuel then flows through the valves and piston and mixes with the oil. The diluted oil will not lubercate and you will sieze the engine.( Not good!)
model type and code of the mower and from the engine. generally it is metal stamped on the engine and the unit model is near the rear of the mower.
Buy a lawn mower engine repair manual at Border's or Barnes & Noble.
very gently, or the mower will get squashed