OK it sounds like you may have had a broken sensor that still operated fine.
The timing chain if it broke or jumped enough teeth to cause it to not run. would sound like the engine is spinning over with little to no resistance, it would also sound like it is spinning over a little faster than normal.
This difference in sound may not be detectable to a average person. a seasoned mechanic butt puckers a little hearing this when they were not wanting to tell their customer their engine is shot.
with a non running engine in a car that has high mileage and no service history, you have to start with the troubleshooting flow chart for your car.
Troubleshooting your car involves test that need to be done in order, while gathering data.
This collected data will lead you to what is wrong with your car.
It is possible for one that doesn't have the required tools and test equipment or knowledge to get hurt or killed while attempting these test. you can also do more damage to the very car your trying to bring back to life.
If you know all this and are willing to risk it anyways lets go for it.
First things first lets check the basics, Oil level, coolant level are they good? does the oil or coolant look like a chocolate milkshake? If everything checks good move on to the next step.
Check the battery cables and connections removing them negative cable first looking for corrosion worn cables etc, if you have a serviceable battery check the fluid level in each cell top off as needed with distilled water to just above the cells Not to the top of the battery.
Verify your battery is fully charged and have a computer safe battery charger on hand because you may be cranking the engine over quite a bit while diagnosing the no start problem.
Check each and every fuse under the dash and under the hood with a computer-Air bag safe test light or DVOM or simply pull each fuse look at it if it is in question test the fuse with a DVOM. Ask questions if needed.
Once your done with all of this and found nothing wrong, it would be time to pull a compression test.
Normally you should disable the fuel pump and ignition system before testing the compression to avoid damaging yourself or the car.
rent a compression test kit from Napa or Auto zone they only charge you for the tools while you have them once you return it you get a full refund.
Remove all the spark plugs insert the correct adapter and gauge crank the engine over holding the throttle wide open until the pressure gauge stops moving up.
Once you get a reading write the numbers down. All your cylinders should read within 25-30 percent of each other, Expect well over 90 psi because 90 psi is the minimum to just fire a air fuel mixture.
Most smaller engines run anywhere from 115 psi to over 200 psi so if they are all at 125 to 150 the engine has compression and is not the problem.
While you have the plugs out inspect them take pictures of what the electrodes look like and post them here. along with your compression readings .
If the plugs still look good reinstall them and anything you removed to do the compression test. while putting the car back together inspect all the parts wires and connectors for anything that looks in question.
If your unsure of something you found suspicious take pictures of it and we will try and clear up the mystery.
Once your car is back together you have to find out what your missing fuel spark or both. this is done with specialized test equipment but not expensive and normally part of Napa or Autozone tool loaner program. so you can have access to them for free as long as you return it when your done.
once you have put the car back together and have put the fuel and ignition system back in order by reinstalling fuses or relays whatever you did to kill these systems during the compression test.
You need to verify you have a signal going to the injectors this test is easy on some cars by disconnecting a injector plugging in a Noid light cranking the car over and look for a flashing light from the Noid tester. if you have a flashing noid light while cranking and fuel pressure at the rail verified with a fuel pressure test.
You can now test for spark using a spark tester that plugs in place of the spark plugs since you have a 4 cylinder its best to have four of them and run a ground wire to each tester and use the attached clamp to make the connection to the provided ground wire.
Others will say you can just use a spark plug and a wire, while this is true it makes it possible to damage the ignition system. So do not make it worse when testing.
I say use four spark testers all at the same time so you can verify not only the car is creating spark to all the cylinders but it is creating it in the proper order.
Once your done with the spark test. you should have the data you need to to start the diagnostics in the correct place.
If your missing spark and pulse to the injectors it may be a bad ICM ignition control module, however their is test procedures specific to your car and it should be followed exactly to avoid replacing parts needlessly.
You may get lucky and fumble across the cause of your problem during all this testing and get it fixed very easily so do not be afraid to stop what your doing make minor repairs as needed and writing down what you did.
to answer your question on how to tell if your timing chain is broken, this can sometimes be done by simply removing your oil cap, if you can see a rocker arm or spring just have someone crank over the engine while you check if the rocker arm is moving. if it is not moving and the engine Lower half is spinning you have either a bad timing chain or broken cam shaft.
If the cam shaft is broken ( not likely at all ) it will be from oil starvation that seized the cam. Normally this would happen while driving and is not very common.
If you cannot see any of the moving parts just move on to the compression test after checking the basics mentioned earlier.
because even if the cam is moving it is very possible the timing chain could have just jumped a few teeth.
Timing chains and belts often break or jump teeth on start up because of the sudden torque applied to the worn belt or chain.
I am not 100 percent sure but I think the Quad four is a non clearance engine which means when the cam and crank gets out of time the pistons will contact the valves, normally destroying the engine.
I went out of my way to provide you with all this information, do what you want with it.
My gut instinct tells me you may have a loose connector or crushed wire during the tune up.
So don't panic just yet. Like I said check the basics, recheck your work. if you find nothing the information I provided will give you an idea of what your up against so you can decide to bring it to a shop or try the repair yourself.
If your going to try it yourself please get a good factory service manual or subscription to Alldata.
People here including me may give you test procedures that may be helpful but if it is not for your exact car the information provided or not provided can lead to waste time and money and put you in harms way.
So take everything I have said with a grain of salt, knowing this is just general information not the gospel from GM
