definitely the transformer, these 12v ones never last long.
remove transformer and put it in the freezer over night then reconnect and it see what happens.
make sure its dry first of course.
Replacing the transformer is well easy and you can get a suitable wattage replacement one from screwfix direct £5.77 , and will take 10 mins to fit this dual replacement max 3 lamps
stupid stuart, November 2008