Complex sentence: When Montreal won the Cup, Myre was included in the team picture and was given a Stanley Cup ring, but his name was left off the Cup, even though he qualified, because he did not dress for any playoff games.
Split into simpler sentences: When Montreal won the Cup, Myre was included in the team picture and was given a Stanley Cup ring. However, his name was left off the Cup, even though he qualified, because he did not dress for any playoff games.