Will not start?

First thing would be to get the part number from the failed part, then use that to see what other Ford vehicles fits. Then use it online and see if maybe there is a used one out there or one left in dealer stock somewhere else. Next would be to look at salvage yards and see if one of the vehicles that it was used on still has the part. If it's the module behind the passenger airbag just be sure that the vehicle you are trying to get one from didn't deploy that bag, in theory it shouldn't have hurt it but why take chances. If it's the module in the steering column, those were used on a lot of other Ford vehicles as well so there should be a few out there yet.

The Ford dealership told me they don't make the part anymore. If I buy a new steering wheel column, will I have to replace anything else?

They may not make the part new, but they are still out there, either used or new. If it's the module in the column with the antenna that reads the key you don't need to buy the complete column as that part is easy to remove and if you only swap the transceiver over you can still use your original keys once the unit is replaced. Many shops can do the repairs, or you can DIY it if you find a you pull it yard with the parts still in it. So don't feel the dealership is the only choice as replacing that part is very easy. The OE part number for it is F5TZ-19A438-A and it fits pretty much every Explorer or Mountaineer from 1996 through 2001 Book time to replace it is one half hour.
You start by disconnecting the ground cable on the battery. Then you block the wheels and turn the key to the run position then push the release button to pull the lock cylinder out. Next take the tilt handle and twist it and pull it out. Now you take a screwdriver and remove the screws that secure the two column covers together. Then remove the covers. Next you need to remove the trim plate below the steering column, for that you remove the hood release, then the screws at the bottom of the panel and remove the panel. Behind it will be another panel that you remove. That one allows access to the wire connection for the module. Now disconnect the module and remove the retainer screw, gently pull the antenna coil out and off the ignition housing and you have it apart. Reverse the process to install the replacement part. However, before you put it all back together, I would install the transceiver and then put the key cylinder back in, connect the battery cable and test that it works before you put it all back together.