To answer your last question first the transformer is built into the clock. There are some things you can check, one being the common wire connections in each valve box. another is using a spare solenoid to check if the panel is sending a signal to the valves by taking each wire of the solenoid and touching one to the common wire terminal and the other to an active station. if you don't get a signal you can try and disconnect the power and backup battery for one minute to reset it. if that fails then the clock has gone bad which I have seen many times.

If it has already been 15 years maybe it`s time to change your controller. I wrote a review on the Rachio 3, which came out this spring and customers seem to like it. You can read my article on it here: https://yourgreenanswers.com/rachio-3-smart-sprinkler-controller/