It sounds like your 'hot water out' valve is closed or off.
I can see in the pic you posted that your 'bypass valve' is open. This is going to allow cold water (blue line) into the hot water line (red line)...so you will get cold water out of the hot water taps when turning them on. it also appears the 'cold water in valve' (blue water line only) is also open (and needs to stay like you have it in the pic above)
Close the 'bypass valve' (handle is perpendicular to the piping when closed). Make sure the 'cold water in' valve stays open......then turn the 'hot water out valve' to different positions to see if it opens up....and you get hot water out of the hot water taps.
The replaced 'hot water valve' is probably where your problem lies. It's not open, and is most likely closed. This would be the scenario that allows cold water into the heater, but no heated water out of the heater. Close the 'bypass valve', and make sure the 'cold water in (blue line only) valve' remains open. Now change the position of your 'hot water out valve' handle till you get hot water from it to your taps.
If you never do get water out from the hot water valve , it could be possibly bad too (but doubtful)
It's also possible you have a check valve on the hot water line that is not opening...but this is usually only if you don't have a manual valve on the 'hot water out' line.