I once had a '94 Mazda B4000 4x4 with a 6" skyjacker suspension lift and 33x12.5 BFG Mudders mounted on Centerline deepdish "BottleCaps". (Sorry, had to write all that). I sunk the dang thing when out mudding one day. I burned out the 4x4 computer that's mounted behind the driver seat behind a piece of plastic and I burned out the push-button 4x4 on the dash. Evidently, they do burn out. Try getting a new switch first. I've seen them on Ebay. Try searching under Mazda as well as Ford (same thing). If that doesn't solve it, look to that 4x4 computer. Those retail for about $1000 but Ebay may have those too.
P.S. I was lucky. I did the advertising for a local Dodge/Mazda dealership and they fixed all that plus they turned my rotors and put in new brake pads on all 4 wheels and changed all my fluids for FREE. Oh, and my Mazda was one day out of warranty when I sunk it.