I have a sears 247 889571 24" snow blower. Start fine. Runs rough, like the choke is on. Choke is off. Fresh gas (ran it dry last spring). Ran 1 tank through with it running very rough. Just as it ran out of gas, it ran smooth for 5 seconds or so. Any ideas?

you could try opening up the idle/mixture screw another turn to make the transmission from idle to throttle better
governors just open the throttle butterfly according to the spring tension setting from the throttle lever

Fuel shut off still off? Fuel filter? Owner's manual troubleshooting?

Why do you say its over heating .Runs for 3 minutes the oil is OK .
Do you understand how the choke works .
bacsicly you prime the mechine in cold condutions 3-4 pumps choke to max throttle at 3 /1/4 .
Start backing off the choke after 3-to4 mins .
The choke shuts the fresh flow down to the engine in cold condutions ware it needs more fuel then air to run.
When the engine starts to get hot it can't run with out fresh air to mix with the gas it won't run anymore because there is to much gas and not enough air
Its simple fool prof will work everytime if you adjust it right

Draining the gas from the tank doesn't drain the float bowl in the carburetor. It still had last year's gas in it. Gas will start to turn to varnish if left sitting 6 to 12 months. You'll probably have to remove the carburetor, disassemble it and clean it out with Gumout carb cleaner or some similar product.
When you get it running and the snow's over and done with, put some Stabil in the gas tank to prevent the gas from converting to varnish and then start it up and run it until that stabilized gas is through the carburetor and into the engine. You can leave it with the treated gas in the tank.

Hmmm... THAT sounds like you have an obstruction (ice???) in the fuel line or in the bottom of the tank.

put in injector cleaner in gas

The bulb usually doesn't feel that way, you're thinking of a small 2-cycle machine where the bulb will fill up with fuel and offer resistance when pushed. A primer on a snowblower is merely to get fuel flowing to the carb from the tank, whereas the bulb on 2-cycle items actually purges air from the fuel circuit. If you keep pressing the primer you should see fuel drip from the carb inlet. Btw, if you see where an air filter might be on other motors, a little metal cup looking thing, try removing the bolts and flipping it over so the fuel drips out easier and snow doesn't have the chance to fall into it if it were facing up. Once you see fuel dripping out, provided you ran it dry last season when you put the blower away and the carb isn't gummed up with varnish, it should start on full choke. Give it about 3-5 seconds and move it to half choke. Once it seems to want to run on its own, open the choke completely and you should be warmed up and ready to go. Also always remember to let engines idle a bit to cool down if you've been running them at high rpms.

if you are using ethanol the check the gas lines for a plug because the ethanol leaves a residue behind that can plug your gas line.

you probably made the mistake of leaving it in the shed over winter with gas in it.
in the carb there is a diaphgram that oumps this fuel in via the motor vibrations.
said diaphgram had been ruptured due to drying gas in the carb. the solver to this is to either have a small engine mechanic replace it or the whole carb or get a new one, and i would suggest you get the cs26 model instead. i have a cs30 and cs26 and i have had less problems with 26. it only has two chokes.
you prime it.
you push lever to start, closing all but a little bit of carb,giving engine much richer mixture.
you squeeze trigger, opens halfway/full, as there are two chokers in the carb, on controlled by lever and another by throttle.basically now you haave half choke.
you release trigger, goes back to 7/8 choke to keep at idle but not running. your ready to go.
on the cs30 its much more complicated:
ful choke
prime 7x.
pull 4x
half choke
pull till start.
wait ten seconds of running at idle rotate to run
good to go. but these guys have porr design. if you take off the back cover and look above fuel tank on cs30, the crank is RIGHT SMACK THERE and not better secured like in the '26 model.
that's what the little circular hole is in it.
anywho, the diaphgram is ruptured, and you probably haven't noticed that in addition you have gas leaking out the carb's air intake.

Drained the fuel tank and rinsed it out with clean fuel then filled with fresh fuel and unit runs fine now.