While unlikely, you can easily test to see if this is a mechanical problem (something wrong with the pipes) or an electrical/controller problem by swapping the wires between Zone 1 and Zone 2. Does the problem follow the wiring, or the Zone. If it stays with Zone 1, then you know it's a problem with the controller.
But since the zone starts up, my 1st guess is that it's going to be something of a mechanical problem, like a busted pipe or busted spray head somewhere. To determine if it's a busted pipe, make sure everything else in the house is turned off (no showers, dish washer, etc) and check the water meter while the controller shows Zone 1 running. If the meter is turning, and nothing is getting irrigated, you obviously have a broken pipe. You might have to let Zone 1 run for an extended period and then look for the soggy spot in the yard.