National Women's History Month
began as a single week and as a local event when, in 1978, Sonoma County, California, sponsored a women's history week to promote the teaching of women's history - a neglected subject in elementary and high school curricula at that time.
a) began as a single week and as a local event when, in 1978, Sonoma County, California, sponsored
b) began as a single week local event sponsoring, in Sonoma County, California,
c) begins with a single week in 1978 sponsoring the local Sonoma County, California of
d) will have began in 1978 as a single week local event when Sonoma County, California was in sponsorship of
e) was begun in 1978 when, in Sonoma County, California, there was to be a sponsorship
The week-long program was a part of a sponsorship event by the County and hence both were simultaneous justifying the use of began. B's mistake lies in implying that the local wee long event sponsored itself. That is what the phrase 'local event sponsoring' without a comma in between indicates.
There is no need to consider other ridiculously structured choices.