Luke Bizzy

I have a '96 Chev. 1500 Silverado Ext. Cab with 4x4. (not a Z71) The 4x4 has been lightly used. It utilizes the push button selector for 2x, 4x4 High and 4x4 Low. When in 2 wheel drive the button light stays steady on. But when selecting either of 4x, the light just blinks and there's no sound of it engaging. I checked and verified that the Transfer Case Fuse didn't blow. Don't know what else to check by myself. What might be the problem? Bad solenoid maybe? Thanks for any suggestions.