No crank no start

I have a 2003 audi a4 1.8t Quattro. The car will only start if I jump the starter solenoid and will only run for a few seconds and shut off. I have a new battery in it and a few relays.

I also replaced the ignition switch. Any ideas and help would be greatly appreciated.

Power from the ignition switch passes through a safety switch, which depends on what kind of transmission you have. If you have an AT transmission try starting it in the neutral position. The engine shut down may be due to a fuel delivery issue. You could try spraying a small amount of starter fluid into the air intake to see if the engine will keep running by doing that. If that works then you need to check the fuel pump operation.