That's a lot of breakages and unless you've been really careless then I can't see how you'd end up with that problem. If you have a digital volt meter then use that to check the continuity of the wires. If you don't have a DVM then they cost very little and you'll need one at some point. If the kids have broken it then sell them; you have to make severe sacrifices to be a good underwater photographer
and while you're at it, if you have any pets have them shot as they tend to shed a lot of flood causing hair. (only kidding)
One thing to remember is that the cable is the weak link. If you aren't 100% careful then water can then get into either your housing or your strobe. This may either short circuit things and fry the electronics, or could end up in a small flood that kills the camera. So I was told that if you do have to take the cable apart to have a thorough dunk test in fresh water - if fresh water gets in you are better off than with saline.
Rob