installed wrong or bad fuel pump
If it has an electric fuel pump you will be able to hear it hum when you turn the car to the run posistion. If you can not hear it hum then its bad. On a mechanical fuel pump you can loosen on of the lines and crank the vehicle. If no fuel comes out the it is bad
yes, no fuel pumping to the engine your car will not crank, be sure it is the fuel pump and not the oil pressure switch or any other problem.
fuel pump or crank sensor
An easy way to prime them is, after the fuel pump and filter are replaced, turn the ignition to on. DON'T CRANK THE ENGINE! When you turn car on, you should hear the pump. Turn car off wait about 5 seconds, and turn on ignition. Do this on and off about 6-8 times, and it should deliver enough fuel to injectors and vent the air.
it needs replacing
Check that the 'new' fuel pump is actually pumping.
testfor badcam or crank sensor. scan car for codes
Your new fuel pump is apparently defective. A fuel pump is required to supply fuel to the engine, and the engine cannot run (and of course not start) without a supply of fuel.
There are many different reasons for that... It can be faulty fuel pump. It can be low pressure in the fuel line. It can be faulty fuel pump relay and etc.
This could be a number of problems... Fuel pump problem? Carbuerator / fuel injection problem? Timing problem?
When replacing car parts it is important to have the diagrams for the wiring. The wiring diagram for the fuel pump of this car can be found in its maintenance manual.
It would help to know what year and model you have but if it is fuel injected try replacing the engine coolant sensor.