From what you said in comment, you "installed" WIII from a backup of your old PC.
Windows, sadly, doesn t work like that, and a lot of thing (register for example) might be missing and end up bugging your game by missing textures.
It could also be a simple DRM, setup set a value in the register, needed to decrypt the model. Since you copied the model but don t have the key, the game ignore the model altogether.
What you should do is find your CD, reinstall from it, or if the CD is unusable but you still have a valid CD-key, go on battlenet, and download WIII/Frozen Throne from there and install properly.
If you don t have your CD(-key) anymore, try to find a friend who still have it, or buy one (I find it regulary for 10€ at video games stores, battlenet price seems to be $15).
I ll add that a key for WIII alone seems to give WIII and Frozen throne in battlenet, but I d like confirmation.