Maya 2010 definitely works with Unity.

There are some caveats:

• Maya supports a bunch of features that Unity and most game engine would not support (like NURBS, hair, dynamically generated effects like smoke)
• You must have the latest Autodesk FBX exporter installed

As elbon96 suggested. First, try exporting your model to FBX manually, then importing that into Unity.

As you noted, the import worked before you made two changes. Please backup your work, undo the changes and redo them one at a time to find the culprit. Perhaps after moving the folders around the links to the material/texture files has been broken. Perhaps the texture file is corrupt.

Also, consider listing what features you added since the last time the model successfully imported.

Unity works fine with Maya 2010. Can you make sure your file associations are correct, i.e. if you double click in your Maya 2010 file (in Windows Explorer) it should open it with Maya 2010.

Does Unity give you any errors when failing to import?

Make sure you set the FBX format option (in the export dialog) to FBX 2009. Then it works flawlessly with Unity. BTW, no need to use an older FBX plugins installer, you can use the latest FBX plugins normally (ie. 2011). It's just the format that you must set to 2009.

Can Maya 2010 export FBX files? I'm not familiar with it, but FBX files have always worked for me.

Well, I installed the FBX plug-in for 2010 but for whatever reason I don't know how to find it....I've watched videos showing people simply going into the file > export and the FBX option and the FBX plug in shows up....it isn't there in my version.