If it does, are you aware of the problem/trick associated with it? That is, try to start your car, after cranking leave the key in the 'ON' position for about ten minutes to reset the key code, turn key off, and then start again.
I forgot to mention, if this is the problem, the "theft" light will be on after trying to start, and you need to wait with key "ON" until it goes out (approx. 10 minutes)
If you are certain the timing belt has not slipped or jumped a tooth after stretching out and you know for certain that it is firing when the piston is near TDC
AND provided you have not somehow re-arranged the plug wires
AND provided the spark is hot enough... If the plugs and wires are correct and the regular ignotion coil is good, you have a pick up coil under the rotor assembly in the distributor...
Let's move onto the fuel system.
How's the filter?
Is Fuel passing through the fuel injectors to the "2.4 'Z-24' engine" ? (Which is a fair engine by the way).
Fuel breaker or fuse is located on the firewall and under the dash (go to the auto parts store to see what the breaker looks like and then search it down), I have seen them in the trunk on Pontiacs...(Under the seats on Range Rovers)...
But let's say your's is good once you find it.
Is the fuel pump in the tank good? Okay, so you're getting fuel and good spark now right?
All that you need is compression with the fire (spark) and the fuel and it should start. It will run with proper timing, etc... But you knew that.
The Z24 Cavalier was a good car when it was under four years old, but after that problems begin to come from nowhere and they are all exactly what you are searching for answers about.
There is never a definate answer with the Cavalier and late 90's GM products.