weedeater doesn't like to come off choke

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?
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I had a similar issue on a weedeater I pulled out of someone else's trash pile, replace the spark plug. it worked like a charm for me.
Dave
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