Welcome to jeepz.com and congratulations on your purchase of your first car , A JEEP !!!!! As posted , the battery will be your first item to tackle . You won't get far with a weak battery on a computer controlled engine . The PCM MUST received proper voltage or many issues will be experienced with things like sensors , electronic injection , ignition , charging system and more. If you find your getting voltage equal to the battery charge at the harness connector to the fuel pump and still no go then it's time to pull the fuel pump . Fortunately , it's easy to pull the pump on an XJ tank. You won't even have to drop it. Just jack up the rear high enough to get under and SAFELY put jack stands under the unibody chassis and allow the rear axle to hang down . You may want to undo the lower shock mounts to allow more drop. The idea is to be able to reach over the rear axle to reach the sending unit retaining ring and remove it to pull out the sending unit/fuel pump. Relieve the pressure in the fuel system first . Clamp off the fuel line to avoid spills , especially onto yourself since you'll be up close and personal with the fuel tank. Before delving into the pump change , do the checks you've researched and as SuoerJ posted , a strong battery is a must. You'll want to be sure what works and what dosen't first and only can be accomplished with a fully charged battery. In addition to any relays and fuses , you'll want to be sure there are no issues with the fuel pump ballast resistor and the ballasted resistor relay . These can easily be missed. Well , sounds like you plate is full but your posts are welcome should you've any questions or wish to share your results . Please remember that if any wiring is to be probed , good chance it may be electrically fed back through the PCM . You'll want to use computer safe test equipment . To start off , I suggest a computer safe test light. A VOM meter that is computer safe is a good investment. I use my trusty action sunpro meter which boasts 10 mega ohm impediance . Translated , that means it only uses 10 mega ohms to feed its digital display and won't over stress the electrical system your testing by trying to draw more colts from it than it normally puts out. That's the purpose of a computer safe test light and all test equipment . They won't exceed the maximum 5 volts that is PCM compliant. 12 volt test lights are a no no here. Save that for your starter and tail light issues . A wiring diagram is a must if you ever feel the circuit may be computer controlled . Pcm's and body control modules control things you'd never suspect are computer related. Your jeep is an '87 so there's far less chance of too much PCM controlled items and won't have a BCM . But do take great care of what computer controlled items it does. I can go on but you get the point. Tread careful and look before you leap. If not sure , ask first , research and/or hit the books. Welcome aboard and thank you for your membership .