Frustration!

This is a photograph of my gas powered cultivator.  I was about to use is yesterday to start the rehabilitation of our lawn, little by little.  But it wouldn't start.  Or, rather it would start and run for 10 seconds and then quit.  It is a Sears cultivator that I have owned for probably 40 years, and has always been difficult to start.  I solved that problem by using winter starter fluid in a spray can - one squirt of the ether into the air intake, and the cultivator would start instantly.  So, yesterday I reluctantly got out all my tools, and began disassembling the cultivator.  Because it would start and run for 10 seconds, I knew that it had to be fuel, and that means the carburetor.  So I took everything apart and disassembled the carburetor.  I cleaned out the passages and checked for dirt and found nothing. So I put it all back together.  It took the better part of the afternoon, which is not what I wanted to do.  I put gas in it, gave it a sprtiz of starter fluid, and it started...  for 10 seconds, and then quit again!  That was maddening!  So this morning I started all over, and took it all apart again, and carefully looked at every part of the carburetor.  I got out my air compressor and blew out all the passages again and double checked everything.  Reassembled it, gassed it up, and, put, put, put, and it died.  So frustrating.