The fuel pump receives power from the fuel pump relay, which in turn is
energized only on the Auto Shutdown (ASD) relay's say-so, which occurs
only when the Single Board Engine Controller (SBEC) gives the go-ahead,
which happens only if:
    -The ignition is switched "on"
    -The SBEC is receiving power
    -The SBEC sees a pulse signal from the hall effect pickup in the
distributor.

Your first diagnostic step is to disconnect the negative battery cable for
two minutes, reconnect it, crank the engine, then check for stored flash
codes.

To check the computer codes:

With the engine off, switch the ignition key on-off-on-off-on,
leaving it "ON". Do not
go to "start", just "on" during this procedure.

Watch the "Check Engine" light.  It will turn on, then go off, then will
begin to flash-out any trouble codes that have been stored. For instance,
if it flashes:

flash <pause> flash flash
<long pause>
flash flash flash <pause> flash flash flash flash flash
<long pause>
flash flash flash flash flash <pause> flash flash flash flash flash

Then you have a 12 (one flash followed by two) a 35 (three and five) and a
55 (five and five).  55 means "end of codes" or, if by itself, "No codes
stored.  Check the codes and report what you find.

"12" means "start of codes" when observed via the dash light.
"55" means "end of codes".

If you get a code "11" (12-11-55), the hall effect pickup in your
distributor has gone and you'll need a replacement.

If you get no codes at all, your SBEC isn't getting power and you've
probably got a corroded wire or a blown fuselink upstream of the SBEC.

If you get other codes, other problems may be indicated (faulty ASD relay,
faulty fuel pump relay).

DS

Auto Fuel Shut-Off switch, located on my 94, behind an interior panel on
the drivers side near the rear wheel. Check your manual for location.  
This must be manually re-set if tripped.

be careful bench testing the pump. its a good way to have a fire, You
needed to check for 12 volts and a good ground at the fuel pump when it
was in the tank,did you do that before removing it? You only have 3
seconds before ASD shuts down the the pump when testing so you may want to
get a second person to turn the key on while you are testing.
It could still be the pump and by taking it out may have gotten  it to
work for the bench test .some times if you hit the bottom of the tank
where the pump is.....it will get the pump running again
Any codes in the memory of the engine controller

On a car as old as yours, you can save a lot of money by bypassing the ASD
relay because to replace the ASD relay you've got to replace the Power
Module, an expensive piece.

Just get a Bosch 20amp lighting relay and wire it in.  Coil energize to
ign. sw., Input to batt., Output to coil +, grnd to grnd.

With this setup, whenever you start the engine, the ignition and pump are
connected.  When you turn the key to off, the ignition and pump are
disconnected.  This is a perfect solution for perfectionists who take
delight in outsmarting Chrysler Corp.