UPDATE:
Robert, thanks for the advice. Did the spark test and got a nice, blue spark. Drained all the old fuel from the lines, though not from the carburetor, and filled the tank with 93 octane (oops) gas from the local pump--the 10% ethanol stuff.
It's still doing the same thing. With a cold engine, here's the progression:
1) Pull starter cord about 10 times with throttle on full choke. Engine starts around the 10th time and revs like normal, then dies within 1-2 seconds.
2) Pull starter cord repeatedly on full choke, maybe 7-8 times, no results.
3) Let mower sit for about 60 seconds.
4) Pull starter cord ONCE on full choke, engine fires right up, and dies within 1-2 seconds.
5) Let mower sit about 60 seconds.
6) Repeat steps 4 and 5 until you have great-grandchildren.
7) :confused3:
Maybe I just don't have all the old fuel out of the bottom of the system, but it seems like after all those starter cord pulls, it should have gone through the cylinder and been burned up when the thing actually fires for a second or two.
I'm close to taking it in to the nearest small-engine shop, but I'd rather keep my $$$ for the grass seed I'll need to overseed my now-sparse and overgrown lawn in September
