mustang 02

My 2002 V6 mustang won't start. It began right after I got home and now it just clicks a single time (starter). I started troubleshooting by checking the starter relay & fuse, replacing them with no luck. Then I tested the battery myself and it read 12.4V with the car off, not bad but this...

So i got a 2002 GT 4.6 V8, for 1500$ its my first buy and i love it even tough its been trashed a little i want to see what you guys think and could suggest me for the best interest of the car, as i already said its been trashed, but i really feel like putting in the work/time/love into this car...