Check your fuses before doing anything.
Before taking anything apart, I would test the diff lock.
Put the truck on 4 jack stands (or two one up front one in the rear, see later why), move the diff lock to "locked" turn the front and rear driveshaft with your hands in opposite directions to try to lock the differential (it probably will be easier to block one wheel and turn the other one.
At some point, the differential should lock. When locked, you will see that your front and rear driveshaft turn in the same direction at the same speed (i.e. wheels turn in the same direction/same speed).
It is does not lock, then this is a mechanical (or linkage) issue. It is does, then this is an electrical issue (fuse, wiring, switch or bulb).
I'm sure a nicer way of testing the diff lock exists somewhere here.
On mine, it was the switch that broke. Could be fixed (and was fixed) but I ordered a (expensive IIRC) replacement. I have yet to get the adjustment right....
1995 D90 NAS
1996 Discovery NAS
2006 LR3 NAS (hers, but comfy! :) )