Service 4wd light on; w4d does not work at all

SOURCE: 4wd not engaging

These trucks are famous for the transfer case control module failing
and causing problems like you are experiencing. The module is
usually located in the passenger foot well kick panel. You should
be able to find it easy since that is what is making the clicking noise
when you try to go into 4x4. When you find it-unplug the 2 connectors
and looks for green corrosion on the terminals in the plug and also on
the module. They are famous for water intrusion thru the heater system. If you find corrosion, terminals in the connectors will need to
be replaced as well as a new module(they are expensive).

SOURCE: My 98 chevy blazer won't shift into 4wd.

Most common problem is the vacuum diaphragm that is so inconviently mounted UNDER the battery tray.The cable that locks in the front diff is attached to it and vacuum pulls it in/out.

SOURCE: 2002 Chevy Trailblazer's 4x4 control

I have a 2002 chevy trailblazer 4x4 control light not working. when trying to switch from 2wd to 4wd nothing happens. no ligth no engaging of the drive

SOURCE: push button 4wd wont engage in 4wd

The solder joints broke on the push button's PC board at the connector. Pop out the button assembly , disconnect from wire harness and re-solder the connector pins to the PC board. Very easy to fix!

SOURCE: My 1999 chevy silverado 1500 four wheel drive

You probably have a bad encoder motor.It is located on the side of the transfer case on the drivers side.It is black.The other problem they had with these was the switch but you have already replaced this so your next thing is the encoder motor.Hope this helps.Good luck.