Do not continue to attempt to force the 4WD Low engagement. This could cause further damage to the transfer case, potentially leading to a much more expensive repair.
Here's what you should do:
* Immediately stop driving in 4WD: Continue driving only in 2WD until you get this issue diagnosed and repaired.
* Professional Diagnosis: Take your vehicle to a qualified mechanic or a dealership specializing in your vehicle's make and model. Describe the symptoms precisely. They'll need to inspect the transfer case to determine the extent of the damage.
* Possible Causes: The problem could be anything from worn gears or bearings within the transfer case to a faulty actuator, low transfer case fluid, or even a problem with the shift linkage. A proper diagnosis is crucial.
* Potential Costs: Repairs could range from a relatively inexpensive fluid change (if that's the only issue) to a very expensive transfer case rebuild or replacement.
Delaying the repair could lead to more extensive damage and higher repair costs. Get it checked out as soon as possible.