Car starts then...

I have a chrysler lebaron 1987.When I start it it comes on for about
half of a second then cuts off.My friends told me it might of been the
fuel pump(electric)

 

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" or "Power Loss" 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.

 

Does the car happen to have any anti-theft from the factory?

 

When I did this,these were the results.It went

Flash<pause>Flash<pause>Flash<pause>Flash Flash<pause>Flash Flash
Flash Flash Flash<pause>Flash Flash Flash Flash Flash<pause>

 

H'mm. 11-12-55. Your hall effect sensor (distributor pickup) is dying
fast. This is a fairly common high-miles cause of a no-start on a 2.2 or
2.5 Mopar. New pickups are not very expensive and can be had from any auto
parts store. Try for a good brand (Standard-Bluestreak, NAPA Echlin,
Mopar, ACDelco...). While you're at it, it's probably time to service the
rest of the ignition. A new cap and rotor, new plug wires, and a set of
NGK ZFR5N or Autolite 385 spark plugs gapped at 0.035".

....(And how long's it been since you serviced the complete PCV system?)

 

So does this means I have to buy a new distributor.Also is this what I
need

http://www.partsamerica.com/product_images/img/NIE/MP825.jpg