Here are the rules about broken sticks based on National Hockey League Official Rules 2009-2010.
Broken Stick – Player
A broken stick is one which, in the opinion of the Referee, is unfit for normal play.
A player without a stick may participate in the game. A player whose stick is broken may participate in the game provided [...]

Until the mid-1980s it was usually accepted that ice hockey was derived from English field hockey and Indian lacrosse and was spread throughout Canada by British soldiers in the mid-1800s. Research then turned up a mention of a hockey very similar to hockey, played in the early 1800s in Nova Scotia by [...]