Im going to say either bad battery cables, bad connections at the battery, bad connections at the starter or possibly a bad battery itself. Thats the kind of crap they'll do when they don't get a solid voltage to the fuel injectors. Also check your grounds.
Or, distributor cap and rotor & spark plugs. They're cheap... start there.
I'll bet if you go through all your connections something is loose. If not, start w/the parts designed to fail like cap & rotor.
Or, IF it only does it when wet, its the coil.