1987 Chevy Silverado Fuel Problem?

New to the forum, and hopefully I can get this issue resolved.

First off the truck is a 1987 Chevrolet Silverado 1500 (G10? K10?) 4x4, 5.7L V8. The engine is *supposedly* new, with less than 8000 miles, but some friends have said that it looks like the original engine. If its the original then it has around 180,000 on it. I have dual gas tanks.

When turning the truck on, it has to crank for a good 5 seconds before actually turning over. Once it turns over, and the key is let go, it dies almost immediately. To get the truck to run the gas pedal has to be pressed down a little just after after it turns over, and it can continue to run after that on its own. Also, until it is really hot, the engine idles up and down. Is this normal?

To me it sounds like the TBI is not getting gas for a little bit after start up. My question is what are the most likely problems, and where can I find them. I have replaced the battery, and cleaned the terminals. I have been told that the engine should turn over almost immediately, and that would be absolutely great if it did. I am really hoping that it is not the fuel pump(s), because we are currently in the midst of another vehicle with a dropped tank and rotted fuel/brake lines. Not fun. Anyway, hope someone can lend some help. Thanks.