Make sure you check your valve boxes out in the yard. It almost sounds like you could have the drain left open (if your boxes are flooded) ... which needs to be shut. Or it is possible that when someone winterized it, that one or more valves were left open (on). Also, sometimes a valve can be manualy left on ... so I usually make sure all the value are turned off (the manual control is off, has nothing to do with the controller signals). Normally, the valves all turn to the left for manual off.

Are you getting water coming out the backflow manifold( the part usually on the outside wall of the house) ? Sometimes you need to replace a plunger there, if you activated the system too early or had it otherwise freeze up during the winter.

You might have some debris from the valve that you replaced and it could of had traveled to the other ones and could be the cause of it. Is the water coming from the sprinklers seeping long after the sprinklers were on? If they are that is a definite sign that you have debris in the diaphragm you can take the top off and clean it up and be sure to flush the valve but don't let any debris back in.

Here is a link that might be useful: seeping