I have attached a circuit diagram. On the lower right you will see the switch, and that it has 3 different resistors in series on each of the three selections possible.
You can either put the switch in each position and use a multimeter to measure for "roughly" that resistance, or you can jumper across the white/light-blue and the gray/red wires to it with a resistor you supply yourself, while the switch is disconnected, to see if that engages the front wheels.
However I would probably start troubleshooting this by having a multimeter hooked up to the brown wire going to the "magnetic clutch control" to see if it is getting 12V (relative to chassis ground) when the switch is in 4Hi or 4Low. That brown wire sends power to the transfer case to engage the front wheels through an electromagnetic clutch coil as seen at the very bottom of the diagram.
Since you aren't getting 4Hi you don't really need to worry about 4low yet.
If you are getting 12V on that brown wire (which can also be accessed at the shift control module to the left of the radio in the dash, you don't have to crawl under the vehicle to get to the upstream portion of that wire run) then you have either an electrical issue down at the transfer case, or at the coil in the case, or something mechanical.
If you aren't getting 12V on that wire, it is time to trace the circuit backwards from that point. Instead of elaborating on that further now, it would be good to know which way you need to trace this further depending on whether there is 12V on the brown wire in 4hi.