Daughters 2005 L series. Need advice.
 

Long story short. Daughter let friend drive while she was visiting Home (Nebraska)Car in Oregon. Friend kept driving after belt broke. Overheated .Took to garage. Said back head needed repair .Replaced belt,plugs, 156,000 miles

I flew in to pick up car Drove to Seattle to get my daughter at my sisters house On the drive(4 hours)I stopped after ,about 2 hrs. car would not start I let it cool down about 30 mins.Started hard. No code lights. Before I got to Seattle low fluid light came on.

Added fluid next day,light went off. Started hard .Drove a couple of towns over .Parked came back hours latter, light came on. Code 0300

Brother in law cleared code. I tried to do drive cycle to get code to come back on .It wouldn't come back .Still starting hard. Had to be back in Nebraska. Drove all day through mountains etc. Plenty of power but at gas stops began to stall.

And start really hard. Engine light finally came on code this time 0340

Spent the night in hotel after driving all day .Now Sunday Am . Put in 1/2 jug of coolant.Took 1 1/2 hours to get started. Began to stall at idle speed .re-start real hard .Now even coasting would stall, I could keep it running by dropping into low gear ,or revving in neutral.

No coolant in oil

Ran good at high speed 75 2100+ miles went through 2 jugs of coolant + 4 bottles of drinking water. Looks like oil down 2 quarts

2005 Saturn L300 v6

Did the head work get done?

WHAT fluid????

.

Did you keep driving that way?

What was oil level when you started?
What was coolant level when you started?

If you're losing that much coolant, the car is likely overheating as you drive and therefore doesn't want to run. Yet you do not describe whether you've observed a coolant leak nor if white smoke is coming from the tailpipe. It's either leaking, boiling off, or burning.

P0300 and P0340 are misfire codes. I'd not put much faith in them right now since the misfiring may have been a result of the more severe issues described above.

I picked up the car from a shop in Corvallis Oregon

Oil was changed -Oil level full
Coolant full

I kept an eye on the temperature it ran steady about half way on gauge

no obvious coolant leaks

White smoke real obvious when I started it in morning it was about 30 degrees out side.Not while driving.

I need more information. Please run both a dry and a wet compression test on her car, and post the numbers here in this thread ....

white smoke out tailpipe often means compromised head gasket -- compression test should shed addl light on the situation

You most likely blew a head gasket by driving it that far with the problems you knew existed. If it got too hot, you may have even cracked a head. The only way you're going to find out for sure is to take it apart.