2001 Audi A4 hard starting

Hi, I am a Newbie to the forum. I have an Audi A4 Quattro 2.8L that starts very hard after it is left for over 8 hours. It can take up to 10-12 starts before it runs continuously and it the meantime it sorts of sputters, shakes and then dies. Once it is running it runs great and I can fully depress the gas pedal without running lean on fuel and if i turn it off and restart it with an hour or 2 no problem. My diagnosis was that I have a low fuel pressure in the rails upon start-up. Since then I have replaced the fuel pressure regulator and it is still not starting correctly. One question I have is that when you put the key into the ignition position should the fuel pump run? Mine is not running. Once it starts up I can hear it running fine. Any help anyone could provide in troubleshooting this would be much appreciated.