Are you referring to the crank or the crank sensor? I don't know about the firing chain on this particular engine, but on my rig, a bad crank sensor will break the firing chain. The rig will act just as you describe in your original post.

While I don't think your timing belt would break simply by going through a water/mud hole, you can check to see if it is still in tact by checking some point on the top end of the engine that would only move while turning the crank if the timing belt was still connected. I'd disconnect the coil packs and pull the fuel relay while doing this, though, if you are going to crank it with the starter.

I'd lay my money on an electrical problem. I don't recommend troubleshooting by changing parts as that gets expensive real quick (been there). Try to get ahold of the literature explaining the firing chain and methodically check the components/connections. Mud/water gets in all kinds of places...

The fact that it cranks without even trying to start leads me to believe that it is probably not a problem at the cylinder level. It is highly unlikely that they all simultaneously failed. I also doubt that you lost compression in all cylinders at the same time. I it's a control problem, but knowing nothing of your engine, I can't help you narrow it down any more than that.

My unsolicited .02...I hope you get it figured out.