Car wont start, changed coils, batt, alternator, CPS,

can be fuel pump, its relay or filter. Could be igniton such as your coil or igntion module.

check timing belt to see if its broken. Check for spark at the plugs. Check for compression with a compression checker from a parts store like Advance or Auto Zone. They will let you borrow it free. The car has to have 3 things. Compression, spark and fuel to start. If one of those 3 is missing, it cant start.

is the batt fully charged-may need to titen cable connects--may be failen batt or alternator--isit gitten fuel--get car scanned from mobile tech

Sounds to me like a bad control module. The control module controls the order of which the coil pack fires. If that is bad you get no spark. Seems to me that it should have been your second option right after replacing the coil pack.

could be the CPS (crankshaft position sensor).

i would have to say first check the fuel injectors fuse in the under hood fuse block if blown replace it,sometimes the fuel injector harness rubs thru anywhere from where the harness comes thru the firewall all the way up to the injectors,,,if fuse is good and no bare wires to injectors,check the wires to the ignition module,,,,and if all checks ok,i would replce the ignition module,,you could have spark from it but it could not be sending the signal back to the pcm to fire the injectors,,,and if all that fails try a pcm,but i think youll find it before that,,i seen this 3 times and each time it was a wire rubbed thru near the fuel rail and it grounds out and blows the injector fuse,
hope this helped

It could be, and almost definitely is very possible its the brain ( ECU or Electronic control module) Will all the things you said it is doing that is probably the problem. Caution : Computer problems are EXPENSIVE

replace engine control module

have it scan it could be many things crank shaft sensor ignition coils and module. idle speed control. egr valve could be stuck open.

sell your saturn