Daewoo was founded in 1967, Daewoo Electronics in 1974.
Daewoo Electronics manufactured the first Korean video game console ever, the MSX based Zemmix in 1985. The system was subsequently upgraded with new revisions until 1991, when the company abandoned the brand. They also licensed the PC-Engine Shuttle in 1990. During the 90's, a few published insignificant games for the PC followed.
Despite its incredible success, the Daewoo group was hit hardest by the big Asian financial crisis in 1997, leading to the disintegration of the group in 1999 and chairman Kim Woochoong (Founder & Chairman Daewoo Group)'s escape to Southeast Asia as a fugitive in a huge fraud affair (he returned to Korea to surrender himself and was sentenced in 2005). Daewoo Electronics went under with the group, but was assimilated into a newly formed company by the same (English) name in 2002. This new company isn't active in the game business at all, though.
Source: http://www.hardcoregaming101.net/korea/part1/company-daewoo.htm