First of all this is not the place for questions, this is for finished unit graphics only. I start to understand the poor admin who has to correct all these wrong posts. I don't know why there are still people posting questions here. You can be sure that your post will be moved.
However, this doesn't solve your problem. You haven't told us exactly which files you have worked on so far. From what you are writing I guess you are trying to add / change a UU (not only a unique graphic for an existing unit) and that you have changed the unitartdefines and the civilizationinfos. If this is the case, you probably missed to add the unitinfos of your unit (to be exactly: an info like you can find it in CIV4UnitInfos.xml). If there is no such file in your mods files, copy it from your Civ games Assets/XML folder. If you are trying to write a modular civ, remove all the entries in that file except of that units entry you'd like to replace with your UU. If you'd like to write an ordinary (nonmodular) mod, simply copy the entry of the unit you want to replace. If you already have a modular mod with a unitinfo file in, copy the entry of the replaced unit from you Civ4 Assets/XML unitinfo file and add it to yours. Read more about modular and nonmodular mod XML work in one of the tutorials. In that unitinfo entry you should now do your changes to the units properties (strength, movement etc.). There should be a line like this:
<Class>UNITCLASS_AXEMAN</Class>
<Type>UNIT_AXEMAN</Type>
Keep the <Class> line, but change UNIT_AXEMAN to UNIT_YOURCIV_AXEMAN or any other name (keep this name in mind). There should also be a reference on your artdefines of your unit, you should correct this. If you have finished your changes to the units stats, open the CIV4CivilizationInfos.xml of your mod. Search for anything like this:
<Units>
<Unit>
<UnitClassType>UNITCLASS_CAVALRY</UnitClassType>
<UnitType>UNIT_WHATEVER_CAVALRY</UnitType>
</Unit>
</Units>
I guess this is familiar to you. It is what you ment when you write
I set the UU portion of that XML to "NONE" so they don't have the dog soldier as their UU.
If I get you right, you changed it to
<Units>
<Unit>
<UnitClassType>NONE</UnitClassType>
<UnitType>NONE</UnitType>
</Unit>
</Units>
If you really want no UU for a civ one day, I suggest changing it to
<Units>
<Unit>
<UnitClassType></UnitClassType>
<UnitType></UnitType>
</Unit>
</Units>
Well, I don't know if your solution (if I really got you right) does work or not, I never tried it, but I would prefer something like I suggested it above. However, in this case you have to change it to
<Units>
<Unit>
<UnitClassType>UNITCLASS_AXEMAN</UnitClassType>
<UnitType>UNIT_YOURCIV_AXEMAN</UnitType>
</Unit>
</Units>
That unittype line depends on what name you have given to your new unit in the unitinfo (that's why I told you keep the name in mind). This should work.
If you only like to add a new graphic to one of your units that depends on the civ you choose, then change the CIV4UnitArtStyleTypeInfos.xml. Copy an entry from the corresponding file of your Civ4/Assets/XML (must be from BtS and this technique will only work for BtS). Search for
<Type>UNIT_ARTSTYLE_WHATEVER</Type>
Change this to
<Type>UNIT_ARTSTYLE_YOURCIV</Type>
Add a
<StyleUnit>
<UnitType>UNIT_AXEMAN</UnitType>
<UnitMeshGroup>
<EarlyArtDefineTag>ART_DEF_UNIT_YOURAXEMAN</EarlyArtDefineTag>
<LateArtDefineTag>ART_DEF_UNIT_YOURAXEMAN</LateArtDefineTag>
<MiddleArtDefineTag>ART_DEF_UNIT_YOURAXEMAN</MiddleArtDefineTag>
</UnitMeshGroup>
</StyleUnit>
This would add a unique graphic for the axeman once we have finished. The 3 artdefine tags refer to your units artdefines. You can have different graphics for different times. You'll sincerly find a tutorial about this if you are interested in doing this. You should remove all other <StyleUnit> entries that are not required. Last step is to change the civilization infos again. Open that file and search for
<ArtStyleType>ARTSTYLE_WHATEVER</ArtStyleType>
Change it to
<ArtStyleType>ARTSTYLE_YOURCIV</ArtStyleType>
Now we are done.
If none of these help you, please report here. Please be more detailed then, for example tell us for which civ4 your mod should be (vanilla, warlords, BtS) and which files you have already changed.