I just bought an old weedeater at a garage sale, when I tried it out
there it started, ran briefly on half choke, then died. I figured it
was worth the couple bucks and brought it home. I have since taken
the whole thing apart, cleaned it up, and reassembled it... all to no
avail. It will cough and sputter on full choke, then rev right up on
half choke but die within 5-15 seconds. If I try to take it off choke
or let go of the throttle trigger it dies instantly. By fiddling
around between full and half choke I managed to get it to run
(sounding fairly decent) for about 45 seconds or so a couple of times.

I'm assuming it's a fuel flow issue. The carb looked quite clean when
I had it apart though and I have played with the screw a bit but don't
know what I'm going for there. Any ideas on what else to do or how to
best adjust the carb screw?