2004 saturn L300 shuts off after you turn on in 4 minutes. what the problem?

I'm guessing you had to remove all the coil to put the new one in. When you reinstalled the coil packs, did you make sure your they are grounded?

Hello, Going from my experience with a 2001 Saturn L300 3.0L V6 & a 2002 Saturn L200 4- 2.2L. They both had similar problems with flickering Lights, headlights dash lights & were hard to move the floor shifter out of park. In both cases the problem was a defective BCM (Body Control Module) You might not be able to buy a new one today & they are very vehicle specific. This is not a plug & play repair, the replacement will need programmed, probably by a GM tech.
There are used ones available at salvage yards or ebay & it would be best to get the part number off the unit, sits on top of the glove box. Good Luck to you & I hope I haved helped.
Thanks, Henry K

Does the engine turn over and not start or does it just click or make no noise at all.

Saturn L-Series - Automatic Transmission Fluid Change ...

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https://www.youtube.com/watch?v=X6Ga3MESkqo
Sep 13, 2013 - Uploaded by DJDevon3
Procedure for changing the ATF in Saturn L-Series vehicles that ... I HAVE A 2004 L300 AND I WAS MAD THAT THEY DID NOT PUT A DIP ...

Saturn L-Series Questions - how do i check transmission ...

Google ecm location 2004 saturn L300, and view images.

If you need further help, reach me via phone at https://www.6ya.com/expert/frankie_091f536560a54e12

Check both relays for the DRLs and headlights for possible sticking contacts and the flash to pass in the multifunction switch may be shorting out .

1. Turn on car

2. Push "clock" button

3. Wait until HR (hour) flashes

4. Look at the "tunes" button at the top right

5. Turn the "tunes" knob (yes, it turns!) left to lower the time or right to raise the time.

Repeat for the minutes

Good Luck!

The starter and or solenoid on your Saturn L300 would need to be replaced. I would first replace the solenoid. When your engine heats up there is too much resistance to allow it to engage. I have seen this problem on 5 other saturns and the solenoid is very inexpensive. Hope this helps!

I've read that these symptoms can be caused by a bad crank position sensor. It is right by the oil filter housing. Maybe it was damaged during the oil change.

Sounds like a crankshaft position senso that is failing when hot.