The only thing that stops water from coming out the hot outlet on WH tank is the check valve.
3 valve system.....no need for check valve
1 and 2 valve systems use check valve to stop backflow when bypassing WH.
Check valve may flow when the hot outlet line is removed but doesn't flow when connected........then check valve is sticking closed.
Check cold inlet open allowing flow to bottom of WH tank.
Then check that bypass is closed
Open the closest faucet---hot side with water source turned ON
Then tap on hot outlet nipple on tank. Still no flow.....remove check valve (just gut the nipple internals) to get hot water flowing.
You can then replace the check valve later or even better.....Install a shutoff valve in hot outlet line and get rid of them junk plastic cheap check valve.