1994 3.3 v6 No spark will not start

If the fuel pump/s continue to run with key on, suspect a relay issue. The relay is grounded by the vehicles computer. If the computer supplies a constant ground, the relay will continue to stay closed and power the fuel pumps constantly. If the the ground wire that comes from the computer to the relay is shorted/grounded, the relay will stay energized as well. As for the no start, are the injectors getting a power and ground supply? The ground side of the injector is controlled by the computer as well. Is the vehicle getting spark at the coil/plug? Have you scanned the computer for any trouble codes?

A fuel pump relay will not effect spark, and you can usually listen to the fuel pump to hear it kick in 1 sec before you crank the vehicle over. Are you sure you are not getting spark? How did you test for spark?

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Did you check the ASD relay and fuel pump relay for power and ground before you replaced those parts ?

CHECK COIL PACK OR FUEL PUMP

If you have to force the fuel pump on by the relay who is controling ignition? The fuel pump will come on thru the main relay which is next to the fuel pump relay this controls ignition,go back to the begining,on one of the coil leave a 1/4 between the sparkplugwire and the coil crank the engine there should be spark is there is no spark correct for spark and fuel will return when the ECM see a valid RPM signal.so test for spark first. The Main relay is what needs to be look at

a) Do you have crank no start? (see entire write up)
b)No crank no start ,No dash lights?, ( battery, battery cables, ignition switch,,starter relay)

If you have symptom A then the affected items are , ignition switch, battery, battery cables, starter, starter relay ,coil, coil pack, ignition module ,Distributor cap ,rotor, (if applicable) spark plugs and wires.
The best thing to do is to first make sure your timing belt didn't break. As long as the engine cranks you can do this. Give the battery a 3 min charge . Then have a helper crank the vehicle while you observe the rotation of all the pulley's and belts. They must rotate together. If the vehicle has a distributor remove the cap, ground the coil wire and remove fuel pump relay ( to disconnect the pump for testing)and watch the rotor as the engine is cranked. it should spin. If this is a-ok your worse nightmare is over.
Now we have eliminated the timing belt as being a cause. We now have to charged the battery again for three min and load test it( this is best done by a repair shop a load tester is expensive .If the battery if more than 5yrs old you may want to replace it.
If battery does not pass load test replace it.
Whatever you decide the rest of the items can NOT be checked out without a fully charged battery.
Check ignition switch and starter relay for B+ going to them and leaving them. Check starter circuit. Make sure B+ is making it to starter ( use a digital voltmeter). If B+ (12 volts) is making it to the starter and it doesn't crank then the starter is defective. Verify this by removing the starter and have it bench tested.
If starter cranks now your into coil testing . First thing reconnect the distributor.
Pull a spark plug, hook it up to a spark tester and ground it, now crank the engine if you get spark coil is ok and in all likelihood so is module.
If you don't get spark test for spark at the coil wire.
If you get spark here and don't get it at the spark plug wire problem is at distributor cap , rotor or spark plug wire. If plugs look bad use a fresh plug to do testing and naturally replace them.
If all of the above are a-ok.
Next is fuel checks. Reinstall fuel pump relay
Easiest fuel check is to put key into ignition cylinder and turn to on position. Lister for pump to buzz or hum. if it doesn't then check fuel pump relay for B+ going to it and leaving it and going to the pump. If B+ making it to pump and it doesn't turn on the pump is your problem. If B+ not making it to pump either the relay or the ignition switch is defective.
Naturally if the pump is defective have a repair shop do the repair . Its dangerous and a real pain.
Good Luck
Now the cutting out after running fora whilrcoild have caused by the coil, ignition module, fuel pump.
We kinda have to get the car to start first to be conclusiveas to why it cuts out.

You need to change the fuel pump.

Likely it's not the pump. but I would check the filter. Spark is controlled on some by a spark control unit, also by a coil inside the distributor that serves as a cam position sensor.
I suggest you get a basic manual like chiltons or haynes and a decent volt/ohm meter and following procedures they outline, test each component.You will spend some money on them but will find them useful many times in the future and far cheaper than guessing and buying parts you don't need. have you checked the pump relay?

have you checked the distributor? When checking for the spark do you pull out one end of the high tension wire (the one connected to the spark plug )and watch (be careful with this one) if there are sparks coming of the end of the high tension wire? If there are none there check out the distributor it may have gone bad or wiring, specifically the ground connector if they are loose or had been disconnected.

If there are sparks in the high tension check the fast idle control valve and the PCV if they need cleaning and the vacuum tubes if there are leaks

Check primary voltage at ignition coil and fuel injectors, engine cranking, use a test lite, dark green wire with orange tracer. If no voltage, that comes from asd relay. Some makes and models if the computer doesn't see the cam and crank sensor signals, the computer won't ground the relay.
You need to do some testing.