You're in California? Anything 1976 or newer needs to be smogged. So cats, all the Nader-junk, needs to go back on. Doesn't sound like there are any exemptions for registration history. I don't live in California, below is just the result of 15 seconds of Googling.
1975 & Older Exempt - Under the old smog laws, 1975 and subsequent model year vehicles became exempt from Smog Check when they turned 30 years old (30-year rolling exemption). A 1976 model year vehicle was exempt in 2005, a 1977 in 2006, etc.
As of April 1, 2005, exempt from smog check requirements are any motor vehicle manufactured prior to the 1976 model year. All vehicles 1976 and newer vehicles will be tested according to state emission law. This law repeals the 30-year rolling exemption.