Do any of the 4wd lights come on or flash?
There is a 20 amp 4WD fuse in the fuse box under the driver side in instrument panel doublecheck this fuse make sure it is good. If you manually shift from
4H to 4L then push the 2-4 does it make any difference. Do any of the lights illuminate? Try doing all of these things while the vehicle is in park then try doing it in neutral and shifting from reverse to drive. Let me know what you find.
Most of the time what you find is the transfer actuator probably is bad. Unfortunately in order to replace this actuator assembly the transfer case has to be removed and disassembled. There is no way to really service the actuator itself it is sold as an assembly.
The shift actuator retails for about $1100. The labor will vary from shop to shop but figure 6.0 to as high as 9.0 hours in labor times your local labor rate which is averaging about 90 or $100 an hour. If you go to www.MetroToyotapartsnow.com you can buy this actuator online for wholesale prices at about $750.
I would take this to a shop and have them try and power up the drive motor on the actuator itself to see if they can force it to start to move. Sometimes if you apply power and ground to the actuator circuit motor itself then tap on the actuator with a hammer sometimes it will jar it loose far enough to allow to shift into four-wheel drive. The actuator on the front differential needs inspect it also.
You are welcome. Your only other option would be to check and inspect the vacuum switching valves located on the driver's inner fender by the power brake booster. These switching valves control vacuum to the actuator on the front differential.