Check valve issue
The valve you found is probably an anti-siphon valve, to allow water one way and then an air break to prevent sucking water back up from the "head" or black tank.
With pressure in the downstream side it sounds like it is plugged downstream of the anti-siphon, or inside the black tank itself. With a drained tank you could try disconnecting the flush line at the tank and seeing it is plugged inside the tank.
If it has not worked since new there may be a number of other things possible wrong but working backwards from the tank itself is the way I would start troubleshooting. Good luck!
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