Cadillac Repair: Cadillac Starter problem, cadillac deville, starter problem

Question
I have a 1997 Cadillac Deville. Over the winter my car refused to start when it got cold (between 10-30 degrees). We tried replacing the battery but that didn't fix the problem. Now even when it's warm out my car will take between 4-10 seconds to crank before it turns over very reluctantly. I recently had a fuel pump go out but the guys at the shop couldn't tell me what would cause it to crank so long after they replaced the pump. What's the problem?

Answer
Have someone listen at the gas cap area with the gas cap OFF.

You turn the ignition switch to the ON position where the dash lights come on, But do NOT try and start the engine. The person at the gas tank should hear the fuel pump run for 2 seconds and then it should stop.

DOES IT ?