Hi, my name is Jerome. I have a 5.7 1989 2500 series...I installed a new distributor, fuel pump and fuel pump relay. My problem is: I have two jump from battery to fuel pump; inorder to get gas to throttle body. I have no injectors working to put gas into motor. Can you help me out.? thank you.

If the battery is dying that quickly you need a new battery
On the Tahoe K series 5.7L the fuel pump relay is in the engine compartment to the rear of the engine control module, should be identified on the cover over the relays
https://fuse-box.info/chevrolet/chevrolet-tahoe-1995-1999-fuses-and-relay

https://scanneranswers.com/signs-of-a-bad-fuel-pump-relay/
https://easyautodiagnostics.com/gm/4.3L-5.0L-5.7L/testing-the-fuel-pump-relay-1

The roll over safety switch may have to be reset. It is in series with fuel pump relay interlock circuit.

You have a fuse / relay box under your hood. My 2002 L100 special edition, 4 cylinder, is located near the battery. You have a relay and a fuse in series. A fuel pump operations check, section 4-3 of the Haynes Saturn L-series 2000 to 2004 manual, you can hear a soft whirring sound for 1 to 2 seconds when you turn the ignition to the ON position. I can confirm mine makes this sound when I do this. Good luck with the fix.

Note, I had a crack in my fuel pump, but I took it to an ex-Saturn dealer 4 or 5 years ago because I did not want to mess with it at the time. They had the part and fixed it in 4 hours, but it also cost me $1000 to replace the fuel pump and install a new fuel filter.

I'm sure you know the fuel pump won't have any affect on the ignition.
You may need a repair book to get the procedures and wiring diagrams to troubleshoot the ignition system.
I am assuming a new coil came with the replacement distributor. Did the cap and rotor get replaced too ?
Do you have voltage going to the distributor coil ?
Is the rotor turning when the engine is cranked ?

it needs more than spark to run! You need compression and fuel too.Try spraying some throttle body cleaner down the intake while someone cronks it.If it runs on the spray,check the fuel sytem(maybe a bad fuel pump,pump relay,blown injector fuse,etc)

For 1999 Buick LeSabre - but you took #1 off the list, so here's the whole "failure to start" list:

Priority Action Part Type Cause
1 Inspect Battery Battery Discharged or Faulty.
2 Inspect Battery Cable Corroded, Broken, Shorted or Poorly Connected Battery Cable.
3 Inspect Distributor Cap Distributor Cap Cracked or Burned.
3 Inspect Fuel Filter Clogged or Dirty Fuel Filter.
5 Inspect Ignition Coil Faulty Ignition Coil.
6 Inspect Wireset Worn, Damaged or Faulty Spark Plug Wire(s).
7 Inspect Spark Plug Incorrectly Gapped or Fouled Spark Plug(s).
8 Inspect Starter Starter Motor Faulty.
9 Inspect Fuel Pump Low Fuel Pressure.
10 Inspect Starter Relay Faulty Starter Starter Relay
11 Inspect Fuel Pump Relay Faulty Fuel Pump Relay.
12 Inspect Fuel Injector Pressure Regulator Faulty Fuel Injector Pressure Regulator.
13 Inspect Ignition Switch Improperly Connected or Faulty Ignition Switch.
14 Inspect Starter Motor Faulty Starter Motor
15 Inspect Fuel Injector Dirty or Worn Fuel Injectors.
16 Inspect Fuel Pump Strainer Clogged or Dirty Fuel Pump Strainer
17 Inspect Engine Control Computer Incorrect Operating Information Being Delivered and Sent From The EEC.
18 Inspect Fuel Tank Fuel Tank Empty.
19 Inspect Carburetor Carburetor Flooded or Faulty Choke.
20 Inspect Distributor Rotor Distributor Rotor broken, burned contacts, or loose
21 Inspect Distributor Worn, Loose, or Incorrectly Installed Distributor.

check your spark. If you have spark check your fuel to see if the pump is working. If there's no spark, check your distributor cap. If there's no fuel check your fuel pump relay and also the emergency cutoff switch on the drivers side in the trunk behind the carpet, make sure its pushed in.

1 Inspect Battery Battery Discharged or Faulty. 2 Inspect Battery Cable Corroded, Broken, Shorted or Poorly Connected Battery Cable. 3 Inspect Distributor Cap Distributor Cap Cracked or Burned. 3 Inspect Fuel Filter Clogged or Dirty Fuel Filter. 5 Inspect Coil - Ignition Faulty Ignition Coil. 6 Inspect Wireset Worn, Damaged or Faulty Spark Plug Wire(s). 7 Inspect Spark Plug Incorrectly Gapped or Fouled Spark Plug(s). 8 Inspect Starter Starter Motor Faulty. 9 Inspect Fuel Pump Low Fuel Pressure. 10 Inspect Solenoid Switch Faulty Starter Solenoid Switch. 11 Inspect Relay - Fuel Pumpat Faulty Fuel Pump Relay. 12 Inspect Fuel Injector Pressure Regulator Faulty Fuel Injector Pressure Regulator. 13 Inspect Ignition Switch Improperly Connected or Faulty Ignition Switch. 14 Inspect Starter Drive Faulty Starter Drive. 15 Inspect Fuel Injector Dirty or Worn Fuel Injectors. 16 Inspect Fuel Pump Strainer Clogged or Dirty Fuel Pump Strainerat. 17 Inspect Engine Control Computer Incorrect Operating Information Being Delivered and Sent From The EEC. 18 Inspect Fuel Tank Fuel Tank Empty. 19 Inspect Carburetor Carburetor Flooded or Faulty Choke. 20 Inspect Distributor Worn, Loose, or Incorrectly Installed Distributor.

Check your fuse and the fuel pump relay.

My 88 ramvan did the same thing and it was the pickup sensor in the distributor. I replaced it and everything was fine. If the sensor is bad it won't let the fuel pump run or the ignition funtion.