“Discombobulate” was one in a series of words invented in the early to mid-1800s as part of a fad popular among educated high-society types who made up faux words by compiling Latin prefixes, suffixes, roots and other non-Latin components into silly-sounding combinations.
Discombobulate itself is used to mean “confused” or “disoriented” now, but originally meant “embarrassed,” “upset,” or generally thrown off. If you knock off the suffixes and prefixes you end up with a nonsense/irrelevant root word (bob or bobule), but that’s not terribly important because the sound of the word was meant to be illustrative of its meaning, and you get the “not with it”/”not (mentally) together” part from dis and com.
Other words in the same curious Victorian vein include absquatulate (“to leave abruptly or run away,” based on a combo of the negative prefix ab- and the component squat, in the “settle/stay” sense), bloviate (blow + orate), obflisticate (probably something like “obfuscate” + “obliterate”), etc.
Featured Image: Day and Night 1938, M.C. Escher