Why does engine shut off and will not start. gas pedal goes down and won't come back up. fuel pump runs. engine turns over?

If your fuel pump is in the gas tank the fuel pump is cooled and lubricated by the gas. If you run out of gas and keep trying to start it many times you can damage the fuel pump. If you have a older car you can try putting a little gas in the carburetor and see if it cranks, if it cranks with gas in carburetor you know it is a lack of fuel problem. You might try spraying starting fluid in air filter but to much can damage your engine. Some links below may provide some help.
https://www.yourmechanic.com/question/car-won-t-start-after-it-ran-out-of-gas-and-was-filled-again
https://www.bimmerforums.com/forum/showthread.php?1881026-Ran-out-of-fuel-now-won-t-start-please-help!
Your vehicle fuel pump can run and pump gas but depending on your vehicle you may not have enough fuel pressure to run. I would check your fuel pump fuse and relay and fuel inertia switch/fuel pump kill switch if you have one. I do not know why running out of gas would cause them to fail but it is something to check.

Sounds like the float level is too low. I assume your pumping the gas pedal to start. This is where the gas allowing the engine to turn over until it uses up the small amount of fuel you added by pumping.

The buzz could be the fuel pump in the gas tank.
If it will run with the throttle open it could have an issue with the idle speed control valve or a dirty throttle body.
The computer controls idle speed by how much air enters the intake thru the valve.

check fuel pump pressure and fuel filter

Try this next time you start it. Turn the key to the run position, do not start the engine. Wait 3-5 seconds and turn the key off. Turn the key right back to the on position and wait for 3-5 seconds. Turn the key off. Repeat the above one more time. Now try to start. If it starts right up you have a fuel supply problem. Either the fuel pump is bleeding off or the fuel pressure regulator is leaking. Pumping the pedal is doing nothing besides buying time for the fuel system to pressurize. Post an engine size and I'll help you locate the fuel pressure regulator. Let me know if you have any questions and I'll do my best to answer them. Thank you for using FixYa.com!

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

try spraying some carb cleaner into a vaccum hose and see if it will run. If so then you have ignition but no fuel delivery. If not then you have an ignition problem. make sure you hear the fuel pump hum when you turn the key to the run position. It should run for +/- 5 seconds then shut off. remove gas cap and listen for fuel pump operation through the fill hole. If you can hear the pump then you have a fuel injection issue. If the engine starts and runs for a few seconds then shuts off then you can suspect the crank or cam position sensor. The fuel pump runs through the oil pressure switch which could also be an issue.

Are you able to start the truck with application of the gas pedal?

check all your rounds on the body, behind kick panels, and in engine compartment. The relays you hear clicking are the power relay whcih turns your engine computer on. The other relay is the fuel pump relay, which is turned on by the engine computer. start there, report back.

PS. When you press the gas pedal to the floor during cranking, it shuts off the fuel supply to clear a flooded engine.

sounds like it is starving for fuel. check fuel pump relay to make certain pump is running. if it is, change fuel filter this may help. the best way to check to see if pump is running is to have someone turn car to on, not start. and feel the vibration at fuel tank with your hand. a pump only runs for a few seconds. until it gets pressure to engine. then when engine is running its on until you shut car back off. you may have to turn key on a few times to feel a vibration. good-day!!

Sounds like fuel delivery problem. I have seen problems such has crud in the gas tank accumulates in the line, blocking it, or some foreign object such as a foil gum wrapper in the gas tank causing the pump inlet to become blocked. After the engine stops running, the blockage eases allowing gas to come through for a bit, enough to start but when the demand for gas goes back up, here comes the blockage again. Could also be a failing fuel pump. Start with easy stuff like a fuel filter change, and I think there are pressure testers where you can check your flow coming into the carb, injectors or whatever you have on that engine. It is nearly 20 years old, many things can and will fail with age and use.

Suggestion, don;t try and start the car with the gas pedal pushed to the floor. Asking for trouble in the future.

Could be a fuel pump, clogged fuel filter.

Check engine light on? If so, Have the code read/scanned at your mechanic, or your local auto parts superstore.