i have an '88 cavalier 2.8 z24.
and having starting issues with her. tried to resolve clogging issues : I've installed new spark plugs, new cat converter, fuel pump, fuel filter. it turns over but still doesn't start. shift light comes on every time it attempts to start. syntec oil, and full tank of gas....just to inform everyone.

any suggestion to trouble shoot or resolutions?

? Have u checked the coil or ignition module.I would say its prob one of two or three things.Either the coil is toast,or the hei module is, or maybe the ESC sensor(knock sensor).The esc sensor is mounted on the block and is called a knock sensor and controls the timing to fire the engine.I would prob replace the ignition stuff 1st unless u check it with a multimeter to varify tolerances based on chiltons/haynes specs in those books or def check to see if the knock sensor is bad which I am pretty sure the 88s had that as a late 1st gen part.Auto zone or advance will show pictures of the part (knock sensor) aka ESC electronic spark control.Being I assume u have fuel going in just no fire,I would lean towards the ignition parts being like over 20 yrs old( probl worn) first b4 the knock sensor.I hope this helps give u some direction and buy a haynes manual for 19.00 covers 82-94 js at both stores above.I say ignition is the issue being the work u have done at this point.But do not rule out the sensor I mentioned the car will turn over for evr and never fire Bc it works in conjuction with the timing.

Get some starting fluid and try that. If it fires up, then it is fuel delivery. If not, it is spark...

Just trying to keep it simple. I overlook the simple stuff all the time.