Q: Engine revs up but will not accelerate when 4wd is engaged, drives fine when not engaged.

According to the 2006 Cherokee Owner’s Manual there were at least two different versions of 4WD installed as a factory option in this model and that is important in terms of the possible causes. Of course, be sure that you have not selected part time 4WD on dry pavement as than can account for the issue you are describing. This includes the 4 Low gear selection. If you have selected full-time 4WD and the car is lugging, that is not changing gears, and accelerating normally, there is probably an electronic control circuit malfunction but the diagnostic decision tree on that is pages long with no "one" component more likely than the other. To resolve this will require an on-site diagnostic and testing and to obtain that the recommended service is a transmission shift diagnostic. If you request that service, the responding certified mechanic will get this diagnosed and resolved, right at your location. If you have further questions or concerns, do not hesitate to re-contact YourMechanic because we want you to make the most of your repair dollars and help you to get the best possible results.