point me in the right direction

[2ball]

My dads John Deere X330 wont start. Its about 3 seasons old.
a couple cuts ago it quit running mid cut and he couldn't get it started.
The air filter was caked with dirt. I cleaned it and the mower started up and ran.

2 weeks later the mower cut out mid cut again. air filter was still clean. It would not start again.
I can get it to start and keep it running with starter fluid in the air intake.

What is my next step?
Clean the carb?
What is the likely culprit?

engine

Briggs & Stratton 44J677
gasoline
2-cylinder
air-cooled vertical-shaft V-Twin
Displacement:	724 cc 44.2 ci
Bore/Stroke:	3.12x2.89 inches 79 x 73 mm
Power (gross):	20 hp

 

[bertsmobile1]

The carb cut out solenoid
Take it out and check that the plunger retracts fully every time you turn the key on.

 

[Rivets]

If the fuel solenoid is working properly, the next thing I would check to see if you have spark when it cuts out. No spark would indicate a hot short or open when the coil heats up. You would then need to replace the coil.

 

[Tinkerer200]

If the fuel solenoid is working properly, the next thing I would check to see if you have spark when it cuts out. No spark would indicate a hot short or open when the coil heats up. You would then need to replace the coil.

Before replacing coil on this engine, disconnect the Kill wire from the base of each coil and see if it starts. More common that diode in Kill Wire Hardness fails than coil.
Walt Conner

 

[2ball]

Thanks for the help guys, this one took an unexpected turn.

I couldn't get the fuel solenoid off, because it was horizontal, not vertical and the flat part of the nut was on the side, so I could not get a wrench in there without taking off the muffler assembly or whatever is on top.
I did unhook the fuel filter and blow (with my mouth) on each side. Gas shot out and it was very red. Turns out when the mower first stopped working Pop's put mystery oil and fuel injection/carb (fuel additive) cleaner in the gas tank.

I drained the tank and put fresh gas in and after about 10 minutes of smoking it settled down and ran fine.

I'm calling it fixed for now.