Did you see a float switch was stuck or is that your first logical assumption?
Are your float switches separate units or integrated in the bilge pump? Was the pump vertical? I don't know what's best but I prefer the integrated style. Fewer connections and theoretically, less likely to stick in the on position due to being in a cage of sorts, protecting it from something floating around in the bilge. Also do you have the constant cycling style or the type that only goes on when the water level rises 2" or so? I prefer the latter...
Are your batteries true deep cycle and in decent condition and are all of your contacts good?
Did it rain like hell all week so the pump ran 24/7?
Also long hoses and corrugated hoses reduce flow causing the pump to draw more power as the discharge takes longer. Father Frank personally undertook this test about a year ago, and posted his findings... I believe the West Marine Pro Bilge series are Johnson products. I have always used Rule products but there are always failures in a saltwater environment. I don't know what's better.
Regarding the dead batteries, you may want to look into a battery isolator. If batteries are tied together on a single switch it is natural that they draw from one another keeping a balanced charge unless they are isolated. Check out this product from Blue Sea Sytems, Im using it and think it's the best system out there for a small boat in big water.
http://bluesea.com/category/2/productline/overview/329
The system protects the starting battery from being drained by the house electronics.