There have been several changes to the way the CPI is calculated over the years. A significant change occurred with respect to weights and hedonic adjustments in 1998 (I believe the pre-1998 series is what ShadowStats, without having any of the underlying data, attempts to replicate), and one in 1983 that, among other things, changed the way that housing services were calculated from an "asset price" approach to a "rental equivalence" approach.
The 1983 change was made to more accurately reflect changes in consumer prices, rather than reflecting changes in asset prices, which is not the point of the CPI. The 1998 change was made in part to more accurately reflect changes in the quality of goods produced, because it had been apparent for some time, particularly in the tech sector, that a computer sold one year for $500 was much more "computer" than the one sold a year or so earlier for the same price, and was therefore actually cheaper in real terms once you accounted for the change in the quality of the goods.
None of the old measures are still tracked, for two reasons:
The old measures were targeted for these changes because they were not believed to accurately reflect economic realities.
Economic statistics agencies like the BLS have limited budgets, and calculating multiple versions of a series is more costly than calculating one version.
So the series you want doesn't exist basically because it'd be a waste of money to have the government calculating numbers that economists believe are wrong.
Old series are dropped all the time for these reasons; for example, around the time of the 1998 change to inflation calculations, the BEA adopted the NAICS industry classification and dropped the SIC system, because the NAICS system was believed to more accurately reflect the structure of industries at the time. For example, before NAICS, computers were in a category called "Industrial And Commercial Machinery And Computer Equipment" right between the pump/compressor/industrial oven category and the industrial refrigerator category. At the same time, guided missiles were lumped into the same category as space vehicles (under transportation), so that we didn't tell the Russians exactly how much we were spending on our intercontinental ballistic missiles (or so I've heard).
However, if you want an independent check on the BLS-calculated CPI numbers, you can check out MIT's Billion Prices Project (a similar project, the "Google Price Index", is no longer publicly available, to my knowledge). You will find that they generally come to the same conclusions as the CPI.