you have probably read the link that was posted, and it is a good one, but you should know a few other options. The factory ESOF system is problematic, and can be a pain as time goes on. Your other SD has manual hubs that were installed, and this is a good fix that usually fixes about 80% of the problem. It is possible that the system has a vacuum problem, and will not disengage. The vacuum problem would suggest that the hubs would not lock either, but anything is possible.
These trucks also have a very poor unit bearing design that is not serviceable, and can also be a pain. I have seen some units made in China that are reasonably priced, but I question the units quality.
The replacement option would be to replace the unit bearing with an eliminator kit from Dynatrac. This kit replaces the unit bearing with an adjustable serviceable bearing, and aftermarket locking hubs. You will have the option of Warn premiums or the newest ones by Dynatrac. The kit can also include stronger 35 spline outer shafts too.
This kit is not the cheapest fix in the world, but very reasonable when you consider all that it has, and all of the upgrades that you get, and all of the hassle that you will eliminate in the future.
You can fix what you have, and maybe it will last for a while, or you can really fix it, and never worry about its performance again. With manual hubs the 4wd syatem will work when you need it.