It's not necessary for a 3 valve WH system to have a check valve......but all your symptoms point to a jammed check valve in HOT outlet (or the shut off valve isn't opening)
The check valve would be inside that fitting right at tank on HOT out.....probably in the straight fitting vs angled fitting. No check valve in shutoff valve.
Turn off water supply...relieve tank pressure via PRV in outside compartment. Then disconnect the screw fitting on angled piece. Turn on water supply (just crack it open) and see if any flow comes out of top fittings. Bucket/towels to stem water drip/flow.
You can remove internals completely and do without the check valve.