1997 Chevy Blazer 4WD

Iwould check the relays under the hood. If not have a friend listen for the motor engaging in the transfer case when you hit the button. Also check fuses.

I would check the connectors at the tranny control module located (usually) behind the right kick panel. The connectors are notorius for being exposed to moisture. DISCONNECT the negative battery cable FIRST before unplugging the module. When you unplug the module, inspect for moisture corrosion on the pins. Sometimes they can be cleaned or you may have to replace the connector that goes into the module.