Complex sentence: The United States women's team did not participate in the 2004 event even though it was the then-reigning world champions; however, it did compete in the 2008 event as FIBA Americas champion.
Split into simpler sentences: The United States women's team did not participate in the 2004 event even though it was the then-reigning world champions. However, they did compete in the 2008 event as the FIBA Americas champion.