Disassembly of the transfer case was discussed in the article Disassembly of the transfer case
Before inspection, thoroughly clean all parts of the transfer case with a brush and scraper, and then wash. Blow off the parts with a jet of compressed air.
Before inspecting the gearbox parts, thoroughly clean them, use a brush or scraper to remove all deposits and clean the holes and splines from possible contamination; then wash (kerosene, solvent, etc.) to remove and dissolve all oil residues.