Replacing engine computer

That's the whole point of using relays. The computer doesn't have to take it. In fact, it couldn't. Think of an elevator. A relay uses a small current supplied by the computer to turn a large current on and off for, in this case, the fuel pump motor. You can't lift ten people, at least not with just one finger, but you can if you use your finger to push the "up" button in the elevator. That's using a small energy to turn a large energy on and off. The computer is your brain and finger muscles. Those don't get damaged if you overload the elevator. The cable snaps, which, in this case would be the fuse!

Now that you know the fuel pump runs for one second, you've proven the pump motor and wiring are okay, the relay contacts are okay, the fuse feeding the relay is okay, the small-current part of the relay is okay, and the computer has control of the relay. All of that circuit is working and it will continue to work if you have spark. I took a jump there but the result is if you have spark during cranking, the same stuff is running that made the fuel pump run for that one second. You need to move on now and check for spark. If it's missing we'll have to diagnose that circuit. I'm basing that on the fact you found 12 volts to the ignition coil earlier while cranking the engine. That means you should have spark but I'll wait to hear back.

Okay, now lets start at the beginning. Step 2 is to determine if the automatic shutdown (ASD) relay is turning on during cranking. I don't have a service manual for your vehicle so you'll have to figure out the wire color we're after. Look for the wire that is the same color at every injector, the ignition coil or coil pack, and the alternator. That is the 12 volt feed wire that comes off the ASD relay. You can measure on any one of those wires. On most car models that is a dark green / orange wire.

You will see 12 volts on that wire for just one second when you turn on the ignition switch. It's easy to miss with a digital voltmeter because they often respond too slowly. A test light might work better. If you don't see that voltage for one second, most likely your test probe isn't making good contact with the terminal. You can back-probe through the back of a connector or you can pull off one injector plug and touch right on the terminal. If you see that voltage, next see if that voltage turns back on during cranking. If it doesn't come back during cranking, the crankshaft position sensor is the first suspect and the camshaft position sensor is the second.