4WD wont' engage

When I try to activate the 4WD on my 1997 Blazer by pushing the button, all I hear is a "click" coming from the front dash area and the 2WD indicator
light stays on. No 4WD. Any suggestions?
Thanks!!
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it could be that the 4x4 actuator under the battery is shot

all
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Possible solution...on my 91, first there is first the vacuum operated unit under the battery, then lines that go to a vacuum switch located in the transfer case activated by a lever....the switch went south. I'm not familiar with your push button system...sounds like there is a solenoid actuator under the dash
Check that the vacuum lines are all attached and working. Maybe use a hand vac pump to actuate the under the battery diaphragm unit and see if the light goes out
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all
I had a similar problem on a 2000 S10 pickup... it turned out to be the encoder motor.
I think that the encoder motor actuates the shift in the transfer case, but I'm not 100% sure.
(If someone would jump in about now and explain the encoder, I'd like to know for sure!)
-NW
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