[Defiant]

The phrase has been around for many centuries, so I don’t think it has to do with machines.

[Vermont Lt]

Machines have been around for a long time. For example a loom can get hung up, as could a plow.

[Red Badger]

http://english.stackexchange.com/questions/31792/what-is-the-origin-of-the-phrase-a-hung-jury

This column by Adam Freedman discusses the phrase:

The Oxford English Dictionary lists the first printed reference to a hung jury in Edwin Bryant’s What I Saw in California (1848-49) in which he states: “The jury . . . were what is called ‘hung’; they could not agree . . .”
Bryant’s phrasing obviously suggests that the phrase was already in common use by the late 1840’s. ... The earliest use of the term in a law report appears in an 1821 case, Evans v. McKinsey. ... it appears that the term developed somewhere in the south during the early 19th Century.
Linguistically, the phrase seems to derive from the sense of “hung” to mean caught, suspended or delayed (“I got hung up at the office”).

[thackney]

Not quite two centuries.

http://english.stackexchange.com/questions/31792/what-is-the-origin-of-the-phrase-a-hung-jury

Another meaning of hung is suspended, and the jury is figuratively suspended as it cannot make a decision.