Following his only complete NHL season, on the day of the 1990 entry draft the Sabres traded Parker to the Winnipeg Jets along with Phil Housley and Scott Arniel for Dale Hawerchuk and an exchange of draft picks seemingly in Buffalo's favour (which became Brad May and Keith Tkachuk).
[4] Devastated about being assigned to the minors, Parker sat out most of the 1990–91 season until he was picked up by the Pittsburgh Penguins as a free agent in February 1991, only to be traded to Hartford along with John Cullen and Zarley Zalapski for Ron Francis, Ulf Samuelsson and Grant Jennings on March 4, 1991.
In his second game with the Whalers on March 12, 1991, against the Washington Capitals, he was checked into the boards and was knocked out for five minutes, resulting in a concussion.
[5][6] He returned to the Whalers two weeks later before sustaining a season-ending knee injury against his former team, the Sabres.
His brain was donated to Boston University to aid in chronic traumatic encephalopathy research.