Is my transfer case broken or is it just the motor to the case?

I had similar deal happen when I accelerated. Truck would do OK 98% of the time except when I really needed the power. Almost got myself & wife killed pulling out in front of traffic on the Interstate and the truck wouldn't go over 45 when I depressed the gas pedal. Wish I could recall what my mechanic did but it was an inexpensive fix: less than $100. It's not your tranny doing this; it's some gadget under the hood. My mechanic did a diagnostic check, was familiar with the idiosyncrasies of Explorers, decided to use a lubricant that had a cleaning effect on the contacts. Truck has run fine ever since. I also own a 1997 Ford Explorer XLT 4WD SUV (bought new). Best purchase I ever made re affordable, dependable SUVs.