Complex sentence: The band made its network television debut in 2000 on "Late Night with Conan O'Brien" and served as the house band on the program "Last Call with Carson Daly" for a short period in 2004.
Split into simpler sentences: The band made its network television debut in 2000 on "Late Night with Conan O'Brien". It also served as the house band on the program "Last Call with Carson Daly" for a short period in 2004.