When someone is stranded in the desert and doesn't know what day shabbat is, he is supposed to count six days and rest the seventh.

We learned an interesting Biur Halacha (Siman 344) this morning that talked about the tefillin aspect. Apparently, even though you rest every seven days, one still needs to put on tefillin each and every day. The reason for this is because since the whole point of resting on the seventh day is just a zecher (you don't really know that that day is shabbat), the din of Rov would apply here. Since MOST days one needs to put on tefillin, we aren't going to exclude this seventh day. However, one does not put it on while saying shabbat prayers, as that becomes a contradiction between the prayer saying that its a day of rest meaning don't put on tefillin, and then going ahead and putting them on.