I changed my fuel pump and change my battery in a 2006 Cadillac CTS and it still won't start what's wrong with it

Why did you change the fuel pump? was there no pressure or low pressure at the fuel rail. What codes are stored on the computer?

Needed replacing the car would start then shut off

Did u ever find out what the problem is

A dirty fuel filter will block the gas. Ice in the fuel lines from took much water from condensation either in the car if it hasn't been used or water in the huge tank in some gas stations. Fuel pumps go bad from people driving with an almost empty tanks as the fuel is the lubricant. Last fuel pump if the car is over 14 -20 years old. When you have a lot of rainy weather in the spring higher grade gas from Mobile (additives not requlated nor required by law so may not be in lower grade gas) . You can add dry gas additive gets the water out especially if your storing the car and the tank is below 1/2 full. Lastly on newer cars with direct fuel injection the injectors can get clogged oropen and close slowly. To clean them and increase gas mileage there is Lucas Gas Treament, 3 Oz per tank.