Indeed yes, that was before the Premier League. So let's look at his record in the following four years after it changed from the 'old' to the 'new' League (with no more back-passes

):
Kenny Dalglish @ Blackburn Rovers 1992-1995 - Div 2: Promotion, PL: 4th, PL 2nd: PL: **Champions**.
Four years later, Blackburn Rovers = relegated. After just one season (yes, a promising start) Roy Hodgson was sacked before christmas he was so bad. Liverpool hiring the guy who relegated former Premier League champions the same year Man Utd won the Treble isn't the wisest decision in my book to bring the glory days back to Andfield. Hodgson at Liverpool has already by-passed the promising first season start he had with Blackburn and has moved straight to his appalling second season results..
Wrong, wrong, wrong decision for Liverpool in so many ways..
Yes, Dalglish has won the Premier League as well as the old First Division. With a team called Blackburn Rovers no less. He's won the title in both the old and the new, the only manager to have done so. Not even Alex Ferguson has managed that, he lost it to Leeds in 1992 (buying Cantona from Leeds in 1993 was his PL success secret imo, can't beat them, buy them..)..