cuppla things:
look in the cavity under the tilting seat - look for a plate/decal with the tractor's full model and serial number info - use that to go to sears parts direct webpage - may be able to d/l an owner's manual at no charge.

If fuel tank is mounted above engine, no fuel pump. if fuel tank mounted under seat (lower than engine carb), then has fuel pump.

also remove and chk fuel tank cap vent for not being plugged up.

post back up here if still probs - should be some more xprt help around here :)

The little vent hole in the center of the fuel cap is a great place to start as rcbe suggested. The very next thing I would do would be to remove the fuel line on the tank side of the filter and lower it to a point that you can catch some inna clean pan to look for debris and check the flow. If by "switching" the filter you meant turning it around, then you probably want to buy a new filter and start over. Debris commonly gets trapped behind the filter, and by running the line, you get much of the debris out. Of course, if the debris went into the side of the filter that is now towards the engine, that isn't good. Beyond the fuel filter is a disc like fuel pump that is above the rh valve cover. They do fail from time to time. You can remove the line aft the pump, set the park brake, crank the engine and fuel should pump out into your catch pan.

IMO when you ran the tank dry you now have air lock or air trapped in the fuel deleivery system. Your tractor probably has fuel pump which is vacuum operated. this is a weak system at most.

You will either have to prime the carb. several times (remove the air filter, throttle half up, no choke, and spray carb. cleaner into the carb. 2 or 3 second blast attempt to start the engine, it should fire off the carb. cleaner for a second or two). Do this several time (4 or 5 atleast) till it pumps fuel up to the carb. on it own) to get it to suck fuel up and push all the air out of the fuel lines. There is another method but not recommended. don't worry about gas in the filter, most of the time they are half empty anyway. I recommend don't run it out of gas cause IMO it makes it real hard to start afterwards.

After four days of rain I tried remoser's starter fluid technique and we are up and running again.
The model # for those who might check this post is 917.276683. Thank you too those who helped me work this out.
Sharon