Kris was asking about when you push the 4x4 button on the dash.
One of the 4x4 problem symptoms is hearing clicks coming from the jack storage box when you push the 4x4 button on your dash.
The control box is in the storage box with the jack. The box is forward of the jack directly over the rear wheel well and is black. There is a white button on the bottom and has two (gray?) connections on the upper left side. The test consists of unplugging the two connections on the upper left side of the control box (not easy, but do-able) and pushing the white button. I don't recall if you have to have the key in the "Acc" position or not, you might try both ways. If you get a solid red light, the problem is with the control board. If you get a flashing light, the problem is your transfer case motor (under the Explorer).
If the test results in a flashing light (thus, a T-case motor problem) there are some good solutions to this if you search under "transfer case" and "4x4". The main extent of the repair work is cleaning and doesn't cost very much at all.
I don't have any experience with the result being steady. I would assume you need to replace the control board.
Another problem people have been having is with their automatic hubs not engaging. This could also cause your problem. If you want to investigate those, just crawl under the car and find the front drivetrain. It will run from the transfer case (in the middle of the truck between the front and rear doors) to the front dif. You should be able to turn it with your bare hands. (You can turn it either way. One will be the right way and one will be the wrong way. The wrong way won't hurt anything) If you turn it the right way and your hubs work correctly, they will engage and you won't be able to turn the drivetrain any more. (If the front wheels were off the ground, the wheels would turn just by you turning the drivetrain) If you turn it both ways and the hubs don't engage (meaning you can turn it freely for several revolutions) then your hubs may be the problem.
Hope that helps.