yesterday, on turning the ignition key, the starter didn't even turn! the dash lights were on. tried a few times, let it rest, then tried again a few minutes later and then it started. what could be the cause?

recently, the car started idling rough (doesn't hold idle well) and still does. The car's electrical seems to have some fault, cos the fuse handling the hazard lights/clock often blows, esp when the weather gets wet. Where should I begin looking? Thanks.