2004 Ford Explorer Starting problem

What do you mean by "then they stop"? The gauges and dash lights stop working or they stop flickering?

There's two things to look at for what you described. The first is the typical loose and corroded battery cable connections. Second, follow the smaller positive battery wire to the under-hood fuse box and be sure that connection is clean and tight. Next, follow the smaller negative battery wire to the body and be sure that one isn't rusty.

Also, don't overlook a failing battery. A professional load test will check for that.

The combination of symptoms suggests there's a defective diode in the generator. That will reduce its maximum current output to exactly one third of its rated full-load current and it will make "ripple" voltage very high. That ripple voltage interferes with computer sensor signals and since the instrument cluster is a computer, it can be affected too. You can unplug the small three-wire connector from the side / back of the generator as a test. If the flickering gauges calm down, have the generator tested.

With one bad diode of the six, you'll lose two thirds of the generator's capacity. That usually isn't enough to run the entire electrical system under all conditions. The battery will have to make up the difference until it slowly runs down over days or weeks.