Lawnmower only starts when I take the Carb cap off and empty it.

[MagwaiGizmo]

My grandmothers lawnmower sat out all winter exposed to the snow and rain. I replace the Spark Plug, Air Filter, and the pull string. Fresh oil and gas in it as well. It wasn't starting when I did all that so I took the bottom cap of the carb which exposed the floater and there was minimal dirt or old gas in there. I put it back on after inspecting a few things and it started up no problem and ran smoothly. Two days after that I primed it and tried to start it again with no luck. Today I decided to take the carb cap off the bottom again and emptied all the gas that was in there. Once again it started up with ease. I'm not too familiar with engines but this seems to be the only way to get it to start up. What could be causing this?

 

[Mikel1]

I would give the carb a cleaning and see if that helps.
If that doesn't help then post your model #'s and what this is on.

 

[MagwaiGizmo]

I would give the carb a cleaning and see if that helps.
If that doesn't help then post your model #'s and what this is on.

Yard Machines Gas Push Mower - Walmart.com

That's the exact engine right there. The carb seems pretty clean but I can't find a diagram to take the carb completely apart as I don't know much about engines.

 

[Mikel1]

What are your engine model and type #'s?

 

[MagwaiGizmo]

UPDATE

I emptied out the fluids and put new stuff in. It ran today for about 10-15 minutes then it just stalled out. I tried restarting it and it kicked over and ran for a few seconds before stalling out again. Continued to do this the next few times I tried. Any ideas?