'03 crown vic pi runs terrible after parked for 4 days while starter is changed.

Give it a tune up, clean throttle body and sensors, clean or replace filters, check for vacuum leaks, PCV, EGR, IAC, test fuel pressure. Running out of gas can be hard on a fuel pump, especially an older one, as fuel in the tank is also used to keep them cool. So your fuel pump may have suffered from constantly running low. I've also had more than one fuel pressure regulator go bad on me with CVPIs. Parts stores only sell those as an assembly, but you can pick up the regulator cheap at a salvage yard. The trick to replacing one without removing the entire fuel rail is to disconnect fuel pump relay while cranking engine to remove all fuel pressure in the rail, then you can pop it off. But I would check all the basic stuff first. Also, some parts stores may lend out a tool like a fuel pressure tester.