Last week I was driving down the road when I.

To check fuel pump relay

Check fuel pump fuse.
Should be able to hear/feel the fuel pump relay click when the ignition switch is turn to the "on" position. Connect a test light to the fuel pump power wire at the fuel pump connector (at the tank). Turn the key to the "on" position. Does the test light illuminate?
If so, the relay is working.
If not, remove relay and check for power at relay socket.
If power is present, with a test light still connected to the fuel pump power wire at the fuel pump connector (at the tank), temporarily connect a fused jumper between terminals 87 and 30 of the relay socket. If the test light at the fuel pump connector comes on replace relay.

Also,

Checking electric fuel pump operation

Verify that the pump doesn't work (listen for it at the tank as an assistant turns the ignition switch on, he/she should close the door and put on the seat belt to eliminate all the bells when the ignition switch is turned on so that you can hear better---do not crank the vehicle), it should run for about 2 seconds. If you don't hear it running, tap on the tank (within the 2 second run time), sometimes this will get it going.
If it still doesn't work, check fuel pump fuse and relay (should be able to feel/hear the relay click when the ignition switch is turned on. Replace any faulty parts found. If everything checks out so far,
Disconnect the wiring connector at the fuel pump and use a test light to check it for voltage when the ignition switch in turned on. If power is there and yet the pump doesn't work the pump is bad.

Check the underhood and inside fuse boxes for the fuel pump Fuse. Theis fuse supplies power to the fuel pump relay.

Recheck the area you worked on. There is a possibility a ground circuit is not secure.
Which engine do you have?

Did you use a testlight or voltmeter to check for power in the fuel pump relay socket?

There is very good info on how to test the relay at this site:

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

When you jump terminals 87 and 30 in the relay socket the fuel pump runs, right?

Does terminal 85 or 86 have power to it with the ignition switch in the "ON" position?

Just to add to this one the sudden gas gauge inop would scare me possibly a body control module failing common on those have replaced a lot of them. Have you seen if you can read codes on it?Also you never mentioned which engine you have?

If the transmission is whinning that bad and leaking sounds like thats a ticking time bomb.

I always look at everything else and the computers being bad last. Did you check all the fuses or just the fuel pump fuse?Also is the security light on solid or flashing when trying to start it or with the key in the run position?