[UsedtobeSmart]

First off, if you haven't already done so, check the transmission fluid to see if the level is at the proper level. While you're doing that you can check to make sure the fluid isn't contaminated, burnt, or compromised in any other way. If the fluid level and quality is fine, and you're sure it's had a relatively recent fluid AND filter change, you may be looking at burnt out bands, bad torque converter, etc. I wouldn't lay the blame on the transfer case as it's an accessory to the transmission.

If the fluid is low, add. If the fluid is high, drain. If the fluid is burnt, do a fluid and filter change. If the fluid is contaminated, you have more serious problems, but at least you're not (hopefully) looking at needing to overhaul or replace the transmission -- either being an expensive proposition. If you don't know how to tell if the fluid is any good, it should be bright red and smell like oil. If it smells or looks burnt, it is.

As for where to take it if the fluid level and quality is fine, or contaminated, most regular mechanics that I know of won't go near a transmission other than replacing a clutch disc on a manual tranny. A transmission repair shop may be your best bet if you don't want to go to a junkyard for a swap -- which has its own potential problems and might not be much if at all cheaper.

Good luck and let us know what you find out.