2002 Chevy S-10 4 WD system

Remove your lower right hand interior kick panel, just below the glove box. Pull up slightly on the flat trim piece going across the lower door frame opening and then pop this kick panel out. There, mounted you will find the Transfer Case Controller. Use a 10mm socket, remove the 3 mounting nuts and pull the controller out a bit so you can get to the connector.
Look at the grey connector lock. Its probably popped out and the pins are not seating all the way. Reseat the grey lock and test your 4X4 buttons. It fixed mine. If this does not do it and you can here this box clicking, more then likely it is the case encoder, mounted front side. Access to that is simple. Remove the little protection plate and then unbolt the encoder. You can pick up a aftermarket for about 120.00 to 200.00.

Goodluck