Sounds like the actuator for the center diff lock has possibly failed in it. Only suggestion is to keep trying it to see if it will eventually start working.
Very likely that the seals between the transfer case and the plastic actuator housing have failed, allowing gear oil to start seeping into the actuator housing and preventing the CDL actuator from working. It's supposed to be completely dry in there. Unfortunately, you can't just pull the actuator housing off to fix it as you will likely never get the timing right again. I've been thru this before. The only proper way to fix it is to drop and split the tcase, replace the seals and ensure the actuator housing is totally dry and that both actuators are working. A new actuator housing runs around $600 I think, so along with labor, very expensive.
My only suggestion, not really helpful right now, is to replace the tcase with one from an FJ Cruiser like I did. Manual shift and never have to worry about failed actuators again. If you can do most of the work yourself, you can do the swap for right around $1000. The FJ tcase is around $250, the expensive part, which will vary pricewise depending on the shop, is getting the driveshafts done. Front shortened, rear lengthened. Mine required all new drive shafts so ran me around $600 for both.
My swap is detailed in my build thread on tacomaworld. Actual swap start mid-way on page 10 -
My daily driver 2003 4Runner Limited 4wd V8 | Page 10 | Tacoma World