No crank, no click, no lights, nothing
 

2005 Edge, 4.0 v6 4x2
I recently replaced the fuel pump and the truck started without issue. Later in the day, it started fine again, but as I was driving I began to lose power. The radio shut off, the wipers slowed (it was raining), and then I lost power to the entire dashboard, each of the gauges went to zero. The engine wasn't producing much power when I pressed on the gas. Then the truck completely shut off. When I turn the ignition, there is no crack or click, and nothing turns on in the start position.
Battery read at 12.7v
Fuse 31 was burnt, so it has been replaced.
The rear ABS speed sensor has also been replaced.

I have searched the forums but I am still unsure of my best course of action. Any advice is appreciated. Thanks.

Any vehicle runs off the alternator when engine is running, ALL voltage comes from alternator

A car battery's only purpose is to start the engine/alternator

Once alternator is working, minimum voltage in the vehicle is 13.5volts, max. is 14.9volts
Car Battery is under 13volts, even new, so voltage flows INTO the battery to keep it charged once alternator is on

From your description the alternator stopped working, did the Battery Light come on BEFORE engine stalled?
It should, if alternator voltage drops to, or below battery voltage, that's why its on when you turn key on before starting

First thing I would do is to disconnect battery cables
Then follow each cable, positive AND Negative, to where they are connected to the vehicle, remove and clean those connections
Then clean battery terminals the cable ends, then reattach

Once cables are attached you will test alternator wires
Key OFF
Use alternators metal case as the ground for volt meter
Test B+ wire on the back of alternator, the big wire, should read Battery Voltage, 12.7v in your case, if lower then a fusible link is blown

Unplug connector, test Yellow/white stripe wire, should have battery voltage, if not fusible link is blown

Test Light Green wire, should be low volts if any
Turn key on
Green wire should no show Battery voltage, if not check Fuse #9 in can fuse box

Thanks for your help RonD. It was the fusible link.

Good work

Thanks for posting the fix