There is no vacuum or electrical gizmos that need to work to engage 4x4, that is strictly a mechanical function that happens solely by pulling the transfer case lever into 4Hi or 4Lo. I suspect your t-case linkage has simply slipped out of adjustment, which often happens after installing a body lift.
The fix only requires that you get under your Jeep with a 1/2" wrench & have someone work the t-case lever while you watch to see how it works. Once you figure it out, you'll see the bolt with the 1/2" head on it. Loosen that bolt, slide the bracket back up the shift rod a tad until it can pull the t-case shift lever far enough to engage 4x4 & then tighten the bolt securely.