84 Z28 Starting Problem

I recently bought an 84 Z28 HO with 4bbl quad-jet carb, 113K miles on engine. Other than some minor cosmetic issues (needs a paint job, few minor dings), it seemed to be in pretty good shape, though it did need some
mechanical work.
So far, I've replaced the shocks & struts (greatly improving the ride), rebuilt the carb (replaced all the gaskets, replaced the valve covers and generally tightened all the bolts, thus fixing a minor oil leak problem), got new wheels/tires (one of the original wheels was bent) and replaced some of the vacuum lines.
The problem I cannot seem to eliminate at the moment is starting it in the morning. Every morning I've got to pump the gas pedal 6-9 times in order to get the engine to turn over. Simply trying to fire it up, or standing on the gas, does no good. Once it has started for the day, it starts right up the first time for the rest of the day.
I've played with the throttle and the fast idle, and the carb rebuild didn't correct the problem either. Any ideas? BTW, I'm not very mechanically saavy... I pretty much have a Chilton's/Hayne's guide strapped to my head anytime I go near the vehicle...
Thanks. Any suggestions are appreciated.
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Make sure the choke is working properly.
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