I have a mower with a 725 EXI engine. I am not a fan of these plastic carburetors I can already say. I took the carburetor apart because it wouldn't start. It didn't appear to be gummed up too badly. Honestly it looked very clean. I went ahead and took everything apart and cleaned it anyway. Tried to start the mower with fresh gas and nothing happens.

I checked the plug see what was going on. The plug was wet so I know fuel is getting to the plug. If I spray carb cleaner into the cylinder and hook everything back up it will start for just a few seconds and then die, so it looks like it is getting spark.

I have tried starting it with and without the air filter and with and without the exhaust on it. It makes no difference. I was really hoping there might be a difference so I could determine that maybe there is some sort of air restriction. But I'm not seeing anything.

Does anyone have any ideas about what else it could be? Thanks in advance!

Did you remove the white plastic insert in the bottom of the carberator?
 
The 3, looks like thin cylinders (face up and down), HAVE TO BE CLEAR.
If you can't spray cleaner thru them that's your issue.  
 
^^ is the most common issue with them.  I did have one with a leaky needle but 
that's pretty rare.  I actually like those carbs as there's no aluminum to varnish up 
or corrode...
 
Lemme find a pic of it..
 
 

 

Yes. I popped it out. It looked good and I cleaned it anyway.

Not to be a butt head (me),
but make sure you spray thru each orifice and it comes out the end..
 
That's about the only thing to "fail" on them..
 
.

I did. I am thinking this is something else. I didn't hit anything that should have sheared the flywheel key, but it is about the only thing I can think of at this point. Is there a specific size key for this engine?

The key is nothing special.  The hardware store should have one that fits...
 
.

Have you tried another spark plug?