Full halo coronal mass ejections (CMEs) erupting from the side of the Sun facing Earth, i.e., frontside full halo CMEs, are considered to be a likely cause of major, transient geomagnetic storms. However, this hypothesis has not been tested over a full solar cycle. We compare all frontside full halo CMEs observed during the first half of solar cycle 23, from 1996 to the end of 2000, with moderate or larger storms at Earth. We show that the association of frontside full halo CMEs with such storms tends to decrease from 1997 to 2000, though this decreasing trend is not monotonic. We examine the locations of the frontside full halo CMEs from 1996 to 2000 with respect to two kinds of coronal closed field regions: bipolar closed field regions between opposite-polarity open field regions and unipolar closed field regions between like-polarity open field regions. We find that even during solar maximum when the occurrence frequency of the two kinds of regions is nearly the same, the central positions of the frontside full halo CMEs are mostly located under the bipolar coronal streamer belt, suggesting that most full halo CMEs originate in the bipolar coronal helmet streamers that are sandwiched between coronal holes having opposite magnetic polarity. Because the inclination of the heliospheric current sheet increases toward solar maximum, the fraction of CMEs emitted into the ecliptic decreases, and the inclination of associated flux ropes increases. These effects help to explain the solar cycle effect on the storm effectiveness of frontside full halo CMEs.