Either of these answers could be your problem, but my money is on Jim's answer.
I would also be hesitant to put a hose down the vent pipe and run water unless you are sure it is empty. You could use a stiff hose to "push" whatever is blocking the vent down into the tank. (maybe a dead squirrel if the cap is gone or a bee nest)
Reasoning for the tank clog:
If the floor of your black tank has a layer of solids that partially blocks the drain valve, fresh solids could plug the valve easily. When you "burp" the hose, you could be pushing the fresh solids up into the tank allowing a "rush" of water to push those solids through the hole.
You sound like a candidate for a RV-Digest-It treatment or two. Use the "clogged tank" instructions on the bottle. RV-Digest-It.com - RV-Digest-It
If the treatment does not solve your problem, a blockage
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW