Originally a teacher, Nørgaard was accepted into the Danish Royal Theater's acting school in 1963, and graduated in 1966. He got his first movie role in the 1966 film Der var engang. Most of his movie roles have been very small parts; a notable exception came in the 1984 movie Drengen der forsvandt where he played a cheating, drunken father whose son ran away from home. He has had many memorable roles on Danish television, such as Niles Nelsen in Bryggeren, Bent Falck in Taxa and many more.
From 1971-1976, Nørgaard was one of two pupeteers on DR's children show Legestue. The show had been on the air in different formats since 1969. This time, it would star a blue parrot named Andrea, performed by Hanne Willumsen, who also created the puppets, and the frog Kaj, performed by Nørgaard. Besides the two puppets, there was a human host named Poul, played by the late singer Poul Kjøller. Besides performing Kaj, Nørgaard would appear in live segments as Poul's dimwitted sidekick, Kjeld. He was also one of the show's writers. The show was a hit, but due to DR's tendency to record over tapes, few episodes survive. The remaining episodes have been in re-run many times since. In 1999, the show was revived as Kaj og Andrea. Nørgaard would return to perform Kaj, and as a co-writer.