Did you do this by any chance? Display > Object Display > Template.
I have an odd problem...I can select one of my objects in Maya unless I select it through the outliner, and even then I can't do anything with it...I can't change it from object mode or anything. And I can still select all the other objects in that scene. I have made sure to check the layer, have looked at the selecting options, made sure "selecting hi-lighting" option is on, and select surface objects lock is on. I have even closed and restarted the program, to no avail. Selecting objects still works for other scenes, so I am guessing that it's an option I accidentally clicked on the object itself? The only thing special on it is a blendShapes.
To untemplate objects
On the Status Line, choose the Select by Hierarchy and Combinations button.
On the Status Line, choose the Select by hierarchy: template button.
Select by hierarchy: template ensures that only templated objects will be affected by a selection.
In the scene view, drag a selection box around all the objects in the scene so that the templated objects are selected simultaneously.
From the main menu, select Display > Object Display > Untemplate.