It went "haywire"; where did this term originate?

Possibly from a farm.

Hay-Food to feed to animals
Wire-Fence to surround animals

They both relate.

I was watching the Axemen on the History Channel, and one of the loggers said that something got caught in the "haywire". Maybe this is the origin

I would imagine that it originated in the begining of the technological revolution. When wires get out of control (like behind most entertainment systems), it looks like a jumble of hay. Or it could be that if you stripped the plastic off of a cable, you'll see a bunch of little wires inside. if a bunch of them frayed, it might really look like hay.

To go haywire is to go out of control; to behave wildly. I have found several suggested origins for this phrase, all from the USA. The first says that wire, properly only intended to bale up hay,(ie haywire) was used, instead, by many farmers to make their boundary fences. The wire rusted quickly with the result that the properties were unkempt and had an appearance of being out of control. A second suggestion says that the wire, when correctly used to bundle up hay, would writhe and wriggle when cut to eventually release the hay. The third says the notion comes from the disorder and chaos present in a farm yard when the used lengths of wire were left dumped in a corner.

From Bartleby; Why should the word for something as functional and mundane as haywire have come to be applied to something that is not functioning properly or to a person who is crazy? It would seem a story of semantics gone haywire. Haywire is a compound of the words hay and wire, originally simply denoting wire used to bale hay or straw. The term is first recorded as a noun in a debate in the Canadian House of Commons (1917), so it is a Canadianism or, since it appeared soon thereafter in a U.S. publication, a North Americanism. We find an earlier (1905) attributive use in the phrase hay wire outfit, a term used contemptuously for poorly equipped loggers. What lies behind this term is the practice of making repairs with haywire. Haywire is found in other contexts with the general sense "makeshift, inefficient," from which come the extended senses "not functioning properly" and "crazy."

From the Scott Polar Research Institute site; "The main party were back in Anarctica in February 1957. An intermediary station was erected at South Ice, 275 miles inland, and on November 24 the crossing was begun in six tracked vehicles with dogs and aircraft in support. Throughout what was to prove one of the "worst journeys in the world", Fuchs maintained absolute discipline and high morale, showing neither depression at delay nor elation at progress. The order in which the cavalcade moved forward never varied: Fuchs was always the leader either in his Sno-Cat, Rock'n'Roll, or in the heavily canvassed areas, probing the way in one of the lighter Weasels."

http://www.phrases.org.uk/bulletin_board/27/messages/1036.html

Wire used in baling hay.
adj. Informal.

1. Mentally confused or erratic; crazy: went haywire over the interminable delays.
2. Not functioning properly; broken.

[From the use of baling wire for makeshift repairs .]

WORD HISTORY Why should the word for something as functional and mundane as haywire have come to be applied to something that is not functioning properly or to a person who is crazy? It would seem a story of semantics gone haywire. Haywire is a compound of the words hay and wire, originally simply denoting wire used to bale hay or straw. The term is first recorded as a noun in a debate in the Canadian House of Commons (1917), so it is a Canadianism or, since it appeared soon thereafter in a U.S. publication, a North Americanism. We find an earlier (1905) attributive use in the phrase hay wire outfit, a term used contemptuously for poorly equipped loggers. What lies behind this term is the practice of making repairs with haywire. Haywire is found in other contexts with the general sense “makeshift, inefficient,” from which come the extended senses “not functioning properly” and “crazy.”

http://www.answers.com/haywire

When wire got into hay and was consumed by a cow, it generally (before magnets) would puncture the cow's belly resulting in death.