Question
we have a four zone sprinkler and zone 3 is not turning on.  The water is not
running while in that zone. Additionally the sprinkler continues to cycle through
the other zones and doesn't turn off.  We replaced the old Toro timer with a new
one but both problems still exist.

Answer
What type of controller did you replace the Toro with? Continuely cycling through zones sounds like a programming situation.
The problem with #3 could be a bad wire or more likely a bad solinoid on the valve.
If you could provide a little more info, I'll do my best to help.

Matt