04 Ford explorer won't start!

First, you have to determine why the key does not engage the solenoid to spin the engine for starting. Start by checking all the fuses related to starting making sure they are good. The non start condition after the starter problem has been solved could be with the fuel deliver system, or power getting to the coil or out the coil via the plug wires to the plugs. A process of elimination.

Checking for a defective coil is simple, easy, and quick with a multi-meter. You just have to obtain the specifications for the coil when doing the test. I am sure there is a video on the net. I recommend, if a coil is needed, purchase a motorcraft one. I've checked other new off brand coils out the box and they are outside Ford's specification.