I know I'm stating the obvious, but there can only be two things either the valve is stuck closed, or you have a blockage.
Everything you did should have fixed the problem which means you either assuming/overlooking something, or not snaking it good enough.
Since you seem to be OK with snaking from the dumping area, I would buy about 10 feet of stiff PEX type tubing. Plumb a hose connection (with shut off) to one end of that tubing, connect the hose to it, open the valve, run the tubing up the line until you hit something, turn on the water and stand back. If you want a little safety, buy an end cap with a hose connection and run the tubing through that hose connection. That way when it give way you only have a 3/4 inch opening to deal with instead of a 4 inch one.
Good luck.
