96 dodge 1500 having problems with my transfer case?

Well to start with, when is the last time you had the T case serviced? It should get serviced every 30,000 miles. I'd start by taking it to a Dodge dealership not a transmission shop. Why pay for someone to rebuild it if that isn't the problem.

Time for a trip to the tranny shop,but first look at the linkage from the shift lever to the transfer case to make sure it is not bent,loose and moving far enough to fully engage.

you can either rebuild that one or replace it with good used one,a rebuilt one cost about 800 bucks so you might want to consider a good used one for 200 bucks,you can still find them that are not to bad on mileage,if you attempt to have this one rebuilt it could get pretty expensive on you,make sure the linkage didn't come loose that will make it try to engage sometimes and cause it to do that,good luck

Time to seek professional help. Also when you have a 4wd you must use it from time to time to keep it in good working order.