I have a 2003 Saturn Vue that won't stay started after we change the starter

SOURCE: 2007 Saturn Vue passlock problem

Take it back to the Saturn Dealer, it is still under warranty.

SOURCE: 2005 Saturn Vue - Starting Problems

make sure to check your fuses and ground wires first. when you are set on which part is bad do a quick check of everything else before you jump into it.

SOURCE: location of the evaporative cannister solenoid? 2003 saturn vue

Depends if the engine is 3.0 or a 2.2?
3.0 purge is on the top, back side of the intake. Black, cylinder. Looks the same on a 2.2, but is located next to the air filter.

SOURCE: 2003 Saturn Vue Alarm - Ignition Kill

Removing the battery cable is something the alarm companies no the theifs can do. Find the valet button, this along with a few steps that you can find with your alarm manual will reset the system.

SOURCE: 2003 saturn vue trouble code p1599

P1599 IS A STALLING ISSUE COULD BE BAD GAS / BAD FUELPUMP DIRTY FUEL FILTER
DISCONNECT BATTERY AND SEE IF THE LIGHT COMES ON AGAIN
U2107 HAS SOMETHING TO DO WITH THE COMPUTER LOOSING POWER AT THE BODY MOUNTS CHECK CABLES AND GROUND STRAP