4WD on the fly system in 1999 Rodeo LSE

When I hit the 4WD button on my 1999 Rodeo it takes over 5 minutes for the light to stop blinking and the actual 4WD to engage. We are getting lots of snow in Chicago this year and I could really use 4WD
going down my unplowed alley. Has anyone else had this kind of problem? Do you know what it could be? We were thinking motor in the transfer case, but I'm not sure. I read the manual and try to stop and push the button and then go forward a little which should make it engage, but it's not working.
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