If your engine is equipped with a fuel shut-off solenoid, 12 VDC will be needed to keep it energized and allowing fuel into the carb...

check for a blown fuse onthe charge system. i blew mine boosting off another tractor and the motor died instantly.

Yeah, may be a fuel solenoid, though it sure quit suddenly when the cables were removed. Seems like it would burn the fuel out of the float for 30 seconds or so before shutdown. The charging system seems to work just fine. There's an amp meter on the dash that seems to work as per normal.

Since you had the neg cable unhooked, you didn't have a ground. 12V to the fuel solenoid, but no ground path.

You misunderstand how the fuel solenoid works.
It doesn't cut fuel off TO the carb. It cuts fuel off from going through the main jet of the carb to prevent after fire, commonly miscalled back fire.

Ahh, OK. These newfangled gadgets are just plain too complicated. I prefer the older models that would run as long as there was a little gas, spark, and air--or maybe even horse drawn. A few oats, a bit of hay, and some clean water--now that was mowing--and no eco worries about the consumption of fossil fuels.