If you can be "discombobulated", is it possible to be "combobulated"?
Solution 1:
It's a slang (originally American) word of unknown origin that goes back well over a century. Probably just a fanciful alliteration of discommode, discomfit, discompose, etc.
It certainly doesn't derive from some pre-existing word combobulate. I think normally you'd be understood if you tried to use that 'back-formation', but I don't think it will catch on.
Solution 2:
In my opinion, it comes from the Italian word "scombussolato", which has the same definition and literally means "of someone whose compass is discomposed or has none". Bussola being the word for compass in Italian.
The alteration of the original word to "discombobulated" follows the classic pattern of enunciation alteration that follow Italian words into English language.
Solution 3:
I can not speak to previous answers. My opinion is based on personal experience. I first heard combobulate/discombobulate (both terms) in the late 1940s from my 60-year-old grandfather, when I was four. On being asked, he could not recall its source.
Several days later, he came to me with a crumbling old letter he had received as a very young boy (mid 1890s), passed down from his grandmother. It was dated in 1823 and written by his great grandfather, and it contained the word combobulate, meaning (from the sense in which it was used) “to make order”.
At the time of writing it, the elder gentleman was in his mid-60s, so I am left to presume that the term goes back a good deal further.