Depends. What kind of material/shader are you using?
Also have a look at your mesh in your modelling application and make sure that the material IDs are set well (in your case all polys should get the ID 1). I also had issues when I exportet a mesh which did not have any material assigned in 3ds Max. So just adding a standard material and on import making sure that “Import Materials” is unchecked did the trick.
That sounds weird. Did you try to attach at least one material in Maya?
Also your problem with the FBX importer sounds strange. It may be a problem with your mesh, or the exporter itself. Did you try upgrading it? You can get the latest available version for your Maya version? Have a peek here: http://usa.autodesk.com/adsk/servlet/pc/item?siteID=123112&id=10775920
I’m not sure though which version is supported by Maya 2010 (Max user here), but I can remember that I had a similar issue with the exporter one day, upgrading helped.
Also you might need to check your mesh, maybe there are some weird modifications on it.
In other words - as long as you are unable to export it via FBX I think there might be something wrong with the mesh itself.