Can a tourist walk into the Parthenon ruins or just around them? Are there any special tours that allow access to the center of the building?
You are required to stay on designated pathways and open spaces. You cannot actually walk inside the Parthenon, just around the perimeter.
Tourists can only walk around the actual ruins of all the monuments (expect the entry monument). There are tours which will give you better insight into the Acropolis but do not go inside. This is part for protection of the ruins and part because they are construction sites.
John: A 3 hour drive (from Louisville) gets you inside the Parthenon (well, the full scale replica at Nashville) - but hey, at the Nashville one you even get to see the 40 ft statue of Athena Parthenos, which has been long gone from the interior of that old ruined one in Athens. :)