The crusty corrosion, while not a good thing, wouldn't cause these problems. It's simply a by product of how batteries work. It can be cleaned off with a baking soda/water mixture and a stiff brush (careful not to get any in your eyes, the crusty stuff is an acid). It sounds like a wiring or fuse/relay problem is the root of your problem. You may have blown a main accessory or ignition fuse, if the car won't even crank (or if it cranks and won't catch). Replacing the fuse may or may not fix your problem, as there was probably some reason the fuse went in the first place (shorted wiring, chafed wire casing, etc). Find a good mechanic with wiring experience to trace the problem (most mechanics around here know engines, but not wiring very well). It may be as simple as replacing a couple inches of wiring, or maybe a connector on the fuse panel. Good luck