When the vehicle is cold it sputters when.

I MESSED UP! THIS IS MY QUESTION! When my Jimmy is cold it sputters for about 15 seconds when I start it. About once a week it will die. After 15 or 20 seconds it runs fine. I've given it a complete tune up. New wires, spark plugs, cap, and rotor. I've replaced the temp sensor. It has a new battery and cables. It isn't throwing any codes. It is a "W" code Jimmy. The standard OBE code testers will not read its computer. It cost over $100 dollars to have it read at the dealer. I don't have that much to spend. Especially when it isn't showing a check engine light. Any ideas. Thanks.

I don't know about the spider fuel system. I've never heard of it. I haven't cleaned the idle air system. I'll look online to see if I can find instruction on how to. I never have cleaned one.