A car should either have spark or not have spark. It will not have spark when it starts, then cut off spark once it is running. Are you checking for spark at the coil or at the end of the spark plug wires (the end that connects to the spark plug)?
Many cars have a crank and a cam sensor. I know on Fords that they are located in the block. If one of these sensors senses something wrong (such as bad timing since you changed the distributor) or is broken, it will send a signal to the PCM to disable spark or fuel so the car will not start. It should not start and then die. It should not start period if something was wrong with one of these sensors.
If you have spark from the coil to the distributor, but not from the distributor to the spark plugs, the timing belt is broken. An easy way to check this is take off the distributor cap and crank the car, if the rotor in the distributor does not turn, the timing belt is broken.
Many cars have a crank and a cam sensor. I know on Fords that they are located in the block. If one of these sensors senses something wrong (such as bad timing since you changed the distributor) or is broken, it will send a signal to the PCM to disable spark or fuel so the car will not start. It should not start and then die. It should not start period if something was wrong with one of these sensors.
If you have spark from the coil to the distributor, but not from the distributor to the spark plugs, the timing belt is broken. An easy way to check this is take off the distributor cap and crank the car, if the rotor in the distributor does not turn, the timing belt is broken.