Weakened by multiple respiratory illnesses, he had just been forced to announce his resignation as conductor last week.
Literal
Multiple respiratory-diseases [cause-による] weakening [reason-のため], he [topic-は] last-week, conductor [as-としての] work [object-を] abandon [content-旨] [possessive-の] announcement [object-を] forced was [just-ばかりでした].
An extremely complex sentence. 複数の呼吸器疾患による衰弱のため gives the reason: 'due to weakening from multiple respiratory diseases.' 余儀なくされた means 'was forced to.' ~ばかりでした means 'had just done.' Dense, formal, news-report style.