I'd be surprised if NASA is using, on a wide-spread basis for missions, computer hardware older than 20 or 25 years at this point. I'm extremely skeptical they are still using much (any?) hardware from the 1960s or 1970s. Your exaggeration goes way too far.
It was an exaggeration, but it seems that the Shuttle was using computers which were a '70s, then a '90s version of a '60s design: https://en.wikipedia.org/wiki/IBM_AP-101 At least the '90s upgrade removed the ferrous core memory.
