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.
Defective fuel pump fuse or fuel pump relay.
No, not if the pump is working.
Check your fuel pressure. No pressure means the pump is not running or defective. Check for voltage at the pump harness and pump relay. If you have voltage and fuel pressure to spec, then you have some other issue, and the fuel pump is not the problem.
installed wrong or bad fuel pump
Blown fuel pump fuse, defective fuel pump relay, or the fuel pump has failed and needs replacing.
You don't. That is very dangerous with a high risk of starting a fire. The correct way of replacing the fuel pump involves removing the fuel tank to access.
Check the fuel pump fuse & relay.
Have someone turn on the ignition without starting the engine while you listen at the fuel filler with the door open and the fuel cap off. You should hear the pump run for a few seconds. If you do then you know the pump is running but it may not be pumping any fuel and may need replacing or the fuel filter is clogged. Replace the fuel filter and if the problem persists then you will have to have a fuel pressure test run on the pump. If you hear nothing then the fuse is blown, fuel pump relay is defective or the pump needs replacing.
yes it will run for a few seconds, then turn off. Its fuel related. More than likely on a 24 year old car the fuel pump needs replacing. But before replacing the fuel pump replace the fuel filter and fuel pump relay. That may solve your problem.
The fuel pump may be defective or the fuel filter may be clogged. Replace the fuel filter if you hear the pump run when you first turn on the ignition without starting the engine. It should run for a few seconds. If you do not hear the pump running, check the fuse and the fuel pump relay. If you hear it run and after replacing the fuel filter you still have no fuel, the pump is defective and must be replaced.
Is the fuel pump actually running. Turn the ignition to the on position without starting the engine and you should hear the pump run for a few seconds. If you do not check the fuel pump fuse and fuel pump relay. If they are both good replace the fuel filter as it may be clogged. Lastly, it is possible that new fuel pump is defective. Check to make sure you wired it back correctly.
If you mean replacing the electric pump with a mechanical one, that is not possible.