Dies out when steping on fuel

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

Which ECM / PCM fuse was burnt ? How did you check fuel pressure ? With a pressure gauge or just pushing the scrader valve an seeing fuel dribble out ? Pull a plug wire an see if there is spark .

Engine Cranks But Does Not Run

Description
The Engine Cranks but Does Not Run diagnostic table assumes that the battery condition and the engine cranking speed are OK. If the battery condition and the cranking speed are not OK, refer to Diagnostic System Check - Engine Electrical in Engine Electrical for diagnosis. Make sure that there is adequate fuel in the fuel tanks.
Diagnostic Aids
• Check the duct work between the mass air flow (MAF) sensor and the throttle body for air leaks.
• A malfunctioning MAF sensor may cause a no start or a stall after start. If you suspect this, disconnect the MAF sensor. The powertrain control module (PCM) will default to the speed density in order to calculate the load and the air flow. If this corrects the condition and the connections are OK, replace the MAF sensor.
If the steps above check OK, refer to Symptoms .
Test Description.

The numbers below refer to the step numbers on the diagnostic table.
It may be necessary to connect a battery charger to the battery for this step. If the battery state of charge is low, the scan tool may reset during the cranking test.
This step tests the ignition relay for proper operation. The ignition relay supplies voltage to the injectors and the ignition coils. When the ignition relay is not operating properly, a no start condition occurs. If the test lamp does not illuminate, this indicates the ignition relay is not suppling a voltage to the fuses.
The crankshaft position (CKP) sensor is located above the starter.
The camshaft position (CMP) sensor is located at the rear of the engine behind the intake manifold.
The ignition feed circuit for the CMP and CKP sensors is internally connected within the PCM. A short to ground on either circuit will cause a no start condition.
The fuel cap may need to be removed in order to hear if the fuel pump is operating.
At this point the engine should start. Refer to Hard Start for further diagnosis.

There is a wire grounding somewhere ,more than likely on the engine.

The fuel pump may have died. Can you hear it turn on briefly, by turning the key to "on"? You may have to stand by the gas tank while someone turns the key to on. It should turn on for about 2 seconds and then stop, after pressurizing the fuel system. If you don't hear it, then check the fuel pump fuse. If the fuse is good, and the pump won't run, one needs to check that the fuel pump wire at the tank connector has battery voltage on it when the engine is cranking-then, you can assume the pump needs replacing.
If the pump is working and you have gas up to the engine, you would next check the ignition system. Start that by checking for spark on one of the spark plug wires.

If the engine won't fire up, but your starter turns over, you may want to check your timing unless you have a check engine light on. If the CEL light is on, have the codes scanned.

If the engine won't turn over with the starter or it clicks, have your battery tested at autozone or advanced auto parts. Replace the battery if it is bad. Else, have your starter tested.

If the engine still won't turn over and the battery and starter are tested fine, you may have a blown fuse, bad ignition switch, or a failed relay.

If the engine fires up but randomly dies and starts back up, you either have a failed sensor, failing fuel pump, clogged fuel filter, bad plugs or wires, or a failing ECU.

I’m happy to help further over the phone at https://www.6ya.com/expert/jeremy_69f3cc28d95bf514

Is your check engine light on?

It sounds like it could be you TPS (throttle position sensor)

If it's not getting the right signal when you step on the gas pedal, it won't let the computer know what position it's in, when the throttle is open it will let in to much air, but not give it enough fuel for that amout of air.....

The fuel heater is connected with the fuel pump, if it does not work, the fuel pump won't pump. Manifold heater has separate relays, fuse, and selenoids which are under the driver battery. If you have been working on it a lot make sure the battery is charged up.

throttle position sensor or a bad fuel pump

That sounds like a fuel issue. You may need to change your fuel pump, fuel filter and either replace or clean the injectors.

if it will crank but not start check the ignition components and fuel pressure if it wont even crank check fuses and all starting system electrical connections and components