The blue wire as said is connected to the "IND" terminal on the alternator and goes to the warning bulb(charge light).
I would obviously fix the loose fuse, but 1 fuse alone won't cause this problem, as the hazzards are on a permanently live circuit(so they work with engine off/key out), the indicators work on position 2.
Make sure the battery is fully charged, and then look at the front indicators bulb holders to see what colour wire is each side, then find these colours at the stalk(indicator switch) put on indicator and see if this side shows live when put on to start with.
The click you hear could be as said simply a flat battery or a stuck/duff solenoid, give the solenoid a good whack first to see if it makes things better.
tabetha