It could be something as simple as a sock or towel stuck under the agetator in the drain hose. Check to make sure before going out and buying another washing machine unless yours is ancient of course. It's likely something minor.
I had an incident of a flood a couple of times with my washing machine. However mine was the result of a slow running sink drain. I have a portable washing machine that I have to pull up to the kitchen sink and connect to the tap and regulate the water temperature by turning on the hot and cold water. If the sink runs slow the water over flows onto the floor. I totally freaked when that happened because I live in an apartment building and I had visions of flooding the apartment below me. Luckily I had some really large bath sheets that soaked up the water quickly.
Is your cat litter the clumping kind? If it isn't you could probably spill it out and spread it out and let it air dry and then use it. Clumping is a lost cause though
I hope there isn't any permanent damage.