It's VERY common for the hubs to not be functioning properly. It's probably not seen any love (grease) for 20 years, and is "stuck" in the unlocked position. Pull the hubs off (it's not hard), disassemble, clean up with your favorite solvent / grease cleaner, then LIGHTLY re-grease it. I like to grease the parts down, then wipe off the access. This is something you should do every couple years (more often if they get submerged regularly, or are otherwise abused).
As said, after you pull the hubs, do the same test you did. If you see axle rotation, it's the hubs. If no axle rotation, it's the diff gears or front axle (not very likely).