Help with 4WD

I just bought a used 1997 chevy Trailblazer Blazer, and I can't get the 4-wheel drive to work. When I press either the 4HI or 4LO buttons to try to engage 4WD, I hear a click noise come from under the truck, and the light on the button I press lights up once (as opposed to blinking or being steadily lit up like it's supposed to). I'm not sure what kind of solanoid I have, so I'm not exactly sure what question I should be asking. Does anyone know how to fix my four wheel drive?

Could be one of 5 or 6 things my problem was the transfer case control module ( computer for the transfer case)

Could be one of 5 or 6 things my problem was the transfer case control module ( computer for the transfer case)

What did You do to fix it?
How much did it cost?

The "click noise from under.." is most likely you transfer case engaging, so the TCCM is probably working. My guess is the front axle is not engaging. Check transfer case switch, vacuum lines to and from transfer case, front axle shift cable, front axle vacuum actuator. There are several other threads with more info. Use the search feature.