Thawed meat can we refreeze
It depends on whether the temperature stayed under 40 F / 4 C the whole time, and even if it did, how long was it above 32 F / 0 C.

If:


Yes, the temperature never rose above refrigerator levels of 40 F / 4C, and
The duration that it was above 32 F / 0 C (above freezing) was not more than the length of time you would normally refrigerate an item (2-3 days meat) then
Yes you can refreeze but the life will be shortened upon being thawed by however long it was above freezing; furthermore, you will probably suffer a loss of quality (especially in texture) from the refreezing cycle.


According the Ohio State University extension, this is likely to only be 24 hours id safety margin assuming you don't open the door.  If you don't know the temperatures, you probably want to be conservative in your estimations.  

After a week, you may wish to lean towards discarding the contents, as sad as that may be.