The OED (2nd edition, 1989) definites byzantine as
"Belonging to Byzantium or Constantinople; also, reminiscent of the manner, style, or spirit of Byzantine politics. Hence, intricate, complicated; inflexible, rigid, unyielding."
Its earliest use to mean intricate, complicated etc. was in 1937. I quote the two earliest citations for this use.
1937 Koestler Spanish Testament iv. 75 In the old days people often smiled at the Byzantine structure of the Spanish Army.
1965 Economist 25 Dec. 1404/3 From the byzantine procedural caution of the approach work [to the Common Market] on both sides, it seems that substantive issues are still beyond the diplomats' grasp.
So, whilst irritating, the meaning has been settling in for a good 65 years now.
Strikingly, the same edition of the OED (1989, remember) doesn't mention any negative connotations for the adjective 'medieval'. As of the earlier 1984 Concise OED, it's also defined as 'old-fashioned'. The Oxford American Dictionary of Current English (1999) * cites the second meaning for the word 'medieval', namely "2. (colloq.) old-fashioned." The Concise OED (2001) ** is even more emphatic: "informal: very old-fashioned or outdated." I don't have any earlier dictionaries handy with which to trace back the 'old-fashioned' meaning, but a handy 1947 thesaurus listed 'medieval', along with things like 'pre-Raphaelite' in its old/ancient section. As of mid-century, the word had 'ye olde time' connotations, but doesn't yet seem to be a synonym even for 'old fashioned.' None of these definitions, however, equate the word with 'barbaric' or anything other than simply 'old.'
Webster's 3rd International (1993) is more forthcoming, and actually offers a source of an early use of this meaning of the word:
"2 : ANTIQUATED, OUTMODED
displayed a medieval carburetor ---Nigel Dennis"
I don't know about you, but I have NO idea who Nigel Dennis is.
Apparently he is also quoted for the following words: faintly, greenhorn, involuntary, megaphone, no-man's-land, nullify, petrify, plainclothes, ponderment, querulous, splay, stumpy, testy, as well as uses of 'to' and 'until'. At a guess, and a look through the local library catalog, he's the Nigel Forbes Dennis, born 1912, and author of a number of literarily-oriented books, plays, and dramatic essays.
At least this means that the 'medieval' as 'old-fashioned' meaning is a twentieth-century one. 'Barbaric' is clearly much, much, much more recent a meaning. The question is - just how much more recent?
* Oxford American Dictionary of Current English (Oxford University Press, 1999. Oxford Reference Online. Oxford University Press. 27 January 2003 <http://www.oxfordreference.com/views/entry.html?subview=main&entry=t21.019042>)
** "medieval" The Concise Oxford Dictionary. Ed. Judy Pearsall. (Oxford University Press, 2001. Oxford Reference Online. Oxford University Press. 27 January 2003 <http://www.oxfordreference.com/views/entry.html?subview=main&entry=t23.034575>)