Fiona McDonald was the lead singer of the 90's industrial rock band Headless Chickens as well as a singer and songwriter for Strawpeople, a band carried on solely by some guy named Paul Casserly. She started her solo career in 2000 with the album A Different Hunger.
Fiona was one of the judges on New Zealand Idol, then she decided that being on TV was awesome, and proceeded to show people art and tell them they look old.
Also, her band wasn't industrial rock, Wikipedia just says that. I would say it's more alternative/pop with a tiny bit of industrial, but you can look them up on YouTube, they've got some really strange music videos. One guy plays a keytar. It's pretty cool.