Outdoor Power Equipment and Small Engines - 20 hp White riding mower not starting

This is a White lawn tractor model GT-2055 with 20hp brigg&stratton engine. Label under seat for numbers has been removed could not find serial number. The mower died real quick while mowing and has not started since. The engine will crank but seems weak. Checked wire to sparkplug and sparkplug, both are sparking. There seemed to be some oil/sludge buildup on sparkplug. Also the starter was recently rebuilt. When I took the air filter case off there is a rubber hose (return line from motor?) that connects to bottom plate of air filter casing that was cracked and finally broke off. Do I need to replace it? There is also a small amount of fuel in bottom of carb right before the choke wing (not sure what it's called). Tried to start again at this point, motor turned over, attempts to start and shoots tiny puffs of smoke out of the broken tube. I'm not real mechanical and just trying to get this working myself. Any tips or advice greatly appreciated.

Yes, you need to replace the hose. It could be causing sufficient vacuum leak to cause the engine to start. You could cap the hose to see if it will start and then replace the hose. Lack of vacuum would cause excessive fuel in the carb.

Which side of the hose is are the puffs of smoke coming from?

your problem could be compresionmy dad fixed a compresion problem there was this ring thing that expands and contracts in heat and cool nes yah definetly replace the tube

The hose has nothing to do with whether it runs or not, but once you get it running, you want to change it because it will suck dirt into the engine if it is broken.

Have you tried new plugs?