So it was a float switch cutting off the condensor? Duh shoulda thought of that.
Cleaning the coil on the inside I would be careful using a hose

might get alot of water in your attic,closet..wherever your furnace and coil is, or air handler or whatever

tons of Air Conditioning units. they make an Aerosal Can of coil clean that works pretty damn well for not needing to rinse it off. Just go to home depot find the can, dooesnt matter which brand . We use whichever is on sale at the time
Inbetween the furnace and the coil should be a metal transition or duct board. cut a hole in it large enough to peel back and fit the can inside. and spray the entire surface down. then turn the unit back on and when it starts creating condensation it will rinse it for you. Can also use a metal brush to get the huge gunk off. On the outside use the hose dont spray tooo hard though or you can bend the fins and that can both make it harder to "breathe" and could straight up puncture it. Sounds like ya got off pretty good though.
Oh also in the main drain from your coil if it doesnt have a Tee in the drain so you can pour bleach into it once a month. Add one. Simple cheap pvc from home depot again and then if you once a month pour bleach in your drain, you wont ever have build up.