Small Engines (Lawn Mowers, etc.): Craftsman snowblower/snow thrower, craftsman snowblower, outer perimeter

Question
We have a Craftsman 3/20 snowblower, model # 536.884231.  It's a 2 cycle, 3 hp pull-start snowblower.  My future father-in-law salvaged it from a curbside collection pile so it has some 'quirks'.  Mostly you have to re-apply the choke when you want it to shut down as the 'off' switch doesn't make a difference.

I'm writing, though, because I am having a problem keeping it running.  I unknowingly ran it out of fuel a while back (checked and there was gas, fired it up and it ran out within seconds and I didn't realize it.)  Before I figured out it was out of fuel, I messed with two screws on the underside of the snowblower.  There's a rounded part exposed through a cutout in the underbody of the snowblower that looks like an oil filter.  (Though I know it's a 2 cycle with oil/gas mixture, so I'm guessing that's not an oil filter.)  There is a screw in the center of this part and a second screw out towards the outer perimeter.  I removed these screws to let fuel drip out, thinking I had flooded the engine.  I replaced them, trying to return them to their original position.

Since then I haven't been able to keep it running for longer than a minute or so with white smoke puffing out of the muffler.  It also runs really rough for that minute.

I've looked at the diagrams but haven't yet found anything looking like the part I've described.

The snowblower was running pretty well prior to my fiddling with these screws.  We did replace the spark plug as the old one was rather rusty.

Any ideas?

Answer
Does your carburetor look like the one in the link below?  According to the model number the carb part number is 640092A.

http://www.smallenginesuppliers.com/shop/html/pages/products/Tecumseh_Carburetor...

The link below is a good repair manual.
http://www.cpdonline.com/692509.pdf
Even though it is for 4 cycle engines, the carbs are the same if you have the carb part number above.

Most likely the carb is dirty.  I would recommend reading the manual and then tackling the carb.  Take digital pictures and notes before and during removal/dis-assembly.  

Let me know if the links help.
Eric