Tried to put the truck in 4 wheel drive last night and it didn't work. Turned the switch and light on dash did not come on and it didn't make the little clicking noise it normally makes. Would this be the switch?

I think you have to put it neutral to do this

Call the dealer.

Switch may be bad. Change switch should fix it.

Just because you charged the battery it doesn't mean it is any good. Modern sealed batteries fail; just as you described, fine one moment and then nothing, they go open internally.

there are 2 systems.
one is a part time system only.the 4x4 locks and is for ice mud and snow.Driving full time will damage the transfer case.The other system is a full time system and the selector says 2wd,4wd part time ,4wd full time and 4 lo. if in full time,it can be driven all the time even on dry roads.The full time is really an all wheel drive system.
the 4low is a very low gear and the main shifter has to be put in neutral and then the transfer case put in 4 low.attempting to put it in 4 low while in "drive" will make a gear grinding noise.
getting out of 4 low is the opposite.shifter to neutral and then put it in 2wd and then in drive.The newer durango has an electronic transfer case with a dial on the dash.The 2002 was available with 2wd,4wd,awd and 4 lo on a switch.The 1999 has the lever on the floor .

If your lights are working correctly on the dash and not just blinking,Double check the hubs are locked in if not automatic ones.

check fuse and relay to switch if power to switch retest switch new doesnt mean not defective if no power check connections and wiring for damage or breaks

the switch on the dash needs to be replaced.

start truck leave in park press 2 wheel high button put truck in drive move truck,check for being in 2 wheel high, if still in 4 wheel low have switch and shift solenoid checked

For you to switch this vehicle from 4 wheel to 2 wheel or 2 to 4. You should follow these steps. TURN VEHICLE ON, PUSH ON BRAKE PUT VEHICLE IN NEUTRAL.STILL HOLDING BRAKE AND VEHICLE IN NEUTRAL PUT VEHICLE IN 4 wheel or 2 wheel if desired. IT SHOULD WORK. Good Luck