The Starting Package Office has moved. The new location is on the same building as before (next to the student union of the University of Turku (TYY), and opposite of Turku School of Economics), just on the second floor.
The address of the Starting Package:
Rehtorinpellonkatu 4B, 2nd floor
Enter the B building using the brownish door, take the small elevator to the second floor, and turn left. You are there!
See the location at the Starting Package Storage's website.