'02 Ford Explorer 4x4 problems

I have a 2002 For Explorer that the 4x4 no longer works. When I push the button to engage the 4x4 the light comes on, but nobody is home!(This means it doesn’t work) The dealership says that it could be in the transfer case, but my regular mechanic says he thinks that it is the motor that engages the 4x4. Either way several hundred dollars to fix, just would like to know which way to go. Any thoughts??

Get a third opinion from an untainted source and go with the majority.