Toyota Repair: 88 Tercel starts then dies, intake manifold gasket, variable venturi

Question
I have an '88 Tercel w/ the 3E engine & variable venturi carb & manual trans. 122,000 mi. The engine will turn over fine & start, then idle for 3 seconds & die.  I can start it & keep flipping the throttle to keep it running badly, then take my foot off the gas & it will idle for 3 secs. & die. I rebuilt the carb w/a kit from O'Reillys & marked all the vacuum lines before disconnecting. Reinstalled & does the exact same thing. Please help, this is driving me up the wall . Thanx !

Answer
These carburetors are difficult to repair and overhaul, so much so, that toyota recommended a long time ago not to attempt it and replace it, there are no parts available from toyota anymore for this carburetor, this was an early attempt at an computer controlled carburetor which turned out to be a disaster and the factory went to fuel injection soon after this.
Assuming that the carburetor is not the problem, it sounds like there could be a vacuum leak, possibly the intake manifold gasket or the base of the carburetor gasket.
Is there a check engine light on, if so please let me know what the trouble codes are and I may be able to help further.