The expression down used to refer to computers is from the mid '60. I think it is an extension of the meaning derived from the term "breakdown" which specifically of machinery, is from 1838:
Down:
- Not working. A computer system is said to be down when it is not available to users. This can occur because it is broken (that is, it has crashed), or because it has been made temporarily unavailable to users so that routine servicing can be performed.
(Webopedia)
- Computer crash sense is from 1965
(Etymonline)
To crash or shut down of computers is from the '70s according to The Dictionary of American Slang,
- to fail suddenly : The spacecraft's No 1 computer ''crashed'' or shut down/ computers that can alert a mainframe owner to an impending computer ''crash'' (1970s+ Computer)