It's one of these 2 things... I've had this before, but I can't remember which of these was the problem. I'm using a Gaelic warrior as an example since that's the only new unit I have on my work computer....
When you go into CivArtDefines_Unit for the unit you'll have these 3 lines
<NIF>Art/Units/GaelicWarrior/Axeman.nif</NIF>
<KFM>Art/Units/GaelicWarrior/Axeman.kfm</KFM>
<SHADERNIF>Art/Units/GaelicWarrior/Axeman_FX.nif</SHADERNIF>
Your new skin is the folder (in this case Gaelic warrior), but you have to rename your skin (dds file) "Axeman" when you put it into your new folder. All of the animations are for Axeman. That should solve it.
Or your problem is that you didn't add the button. It's located here
assets\art\Interface\Buttons\Units
And is simply a copy of your dds file. When you define the unit in CivUnitInfos.xml there is an entry way at the bottom called button. You need to tell the game to find your new button.