What would happen if you gave a patient 2L IV distilled water?

It doesn't come that way. You don't give "distilled" water IV. The usual IV fluids are Normal Saline (NS) , Ringer's Lactate, or a variety of mixtures with 5% Dextrose & Water,10%DW , 5% D/ N, 5% D/1/2 NS, etc. I've never seen any of the mixtures containing distilled water.