I think they are spinning a yarn! That sounds like an electronics glitch. Failing compressors make a noise and although they are electronically controlled, they are just a mechanical pump. You say it spins okay, and the belts look fine. Does the AC work and blows chilled air?
The way to remove it is to fit a bypass pulley. This fits in place of the compressor and uses the same belt and routing. My advice is keep driving it. If it happens again, find an auto electrician. Most have a mobile service.
$189 for a remanufactured compressor on eBay.
https://www.ebay.com/b/A-C-Compressors-Clutches-for-2009-for-Saturn-Aura/33543/bn_87216684
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Out of box bad replacement thermostat, thermostat is backwards, bad water pump, failing radiator (someone may have used a stop leak or ran it it with straight water causing rust build up), fan isnt working or theres a leak and you don't have enough fluid in it.
most auto stores dont carry on shelf have to order or order one online dont need part number just search front motor mount 07 vue need as well if awd or 2wd average price $25+ with auto stores can order online and have delivered or will be notified when ready for pick up usually a day or 2
Take it into a garage. They have a sighting board that is stood about 20 feet in front of the vehicle and has a beam target to adjust into. The headlamp unit has a screw for vertical alignment and another for lateral alignment. It is a 10 minute job.
There is help here
https://www.google.com/search?q=2006+saturn+vue+headlight+alignment+specs
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Water in the electrics of the engoine compartment. Leavng with the battery disconnected for a couple of days may get it goind again if there is no permanent damage.
You won't do that again in a hurry will you.
Check for a shorted or grounded fuel injector the test light will flash but there's not enough current to move the injector. Use a DVOM check that they're all the same.
You may well have ruined the fuel pump. They rely on fuel for lubrication and cooling. Have the fuel pressure checked. You can also try bleeding the fuel at the fuel rail in the engine.