I started my lawn boy mower model 10642C near the cage part on the side it started to smoke and smell like something was burning.

Sara, it sounds like you have come close to burning out the clutch.

Is the carb flooding?is there black smoke coming from exhaust when running, if so it could be the carb over filling with fuel. Is there petrol leaking out of the carb? If not check the fuel pipe is in good condition

Smoke can be a sign of 2 possibilities and one being oil the other being that you flooded it... as for the electrical smell is it coming from the starter from tryin to start it for to long. Careful you could burn up your starter thats never good just give some time between trying and keepthe trying short very short

the engine has been tipped the wrong way oil now in chamber and will burn off eventually

sounds like it broke a ring to fix better to buy new moter not worth trying to fix

the smoke my not smell like gas but check the oil it might the needle valves don't seat in the carb and the gas drains into the crank case and the oil being thinned out by gas can make it smoke nest to check is a blown head gasket they blow out between the cylinder and the lifter port and **** oil into the cylinder its about a $25 part no fancy tools needed just do the one with the low compression

Check head gasket hopefully that is only problem.

valves bad need valve job

The 10640 model does not have an electric start that I can see. Are you sure you have to model number correct? The 10642 and 10642C models are electric start. I will use the 10642 as a parts reference.

The electrical assembly is here:
http://www.partstree.com/parts/?lc=lawn_boy&mn=10642%2C+20in+Mulching%2FRear+Bagging+Lawn+Mower%2C+2009+%28SN+290000001-290999999%29&dn=3361337A-392215-0007

Where did you pull the wires out from? The battery box? The mower harness? The switch?
From looking at the parts available you should be able to figure out which part you need to replace.

Kelly

Check the air breather. Make sure it is clean.

If it is clean, you will probably need to replace the diaphragm. A bad diaphragm will cause black smoke and also cause the mower to run erratically.

Jim