Sorry to say but this is not something that will be on drawings where we can look at what should happen. It is something that has been built, rather than the "Normal" bypass from new.
I'm thinking cold in on the bottom , hot out on the upper line?
So it may take a bit more trouble to find what has been built. But not impossible to sort out with using some ideas.
I would go about it like this.
First I would want to know that water is getting into the tank. To do that I would open some valve or vent on the tank to see water come out. I assume they did leave the pressure and temperature safety valve? That is one easy place to open the tank by flipping the handle up and leaving it as you turn on water pressure from a hose.
Turn on the hose and if water comes out the relief valve, you know water is getting IN! Close the valve again.
One reason to check each step is that the problem may be the valve settings OR it can also be a failed check valve along one of the lines, in or out. Those check valves were often on or very near the back of the heater. Can you spot anything that appears to be a check valve? Just something to be aware of if valve settings don't clear the problem?
I think the valve on these drawings is V6, so it may help to spot one if you have it near the same??
Click these snips to get a better view!
These drawings are the originail as built. First is option 53 J without bypass.
Second is the OEM with option 53Q which has the bypass ( winterize) added.
Best I can see, neither are what you have, so some testing/guessing is needed!
If doing this with cold water, you may be able to feel the tubing get cooler as the water flows and that can help ID in and out?
Once you have ID'd the in, look at the valve on that line to spot which way is closed and which open. Normally I think of the handle as an indicator for this. Aligned with the pipe being open, across the pipe closed? You may or may not have a valve on the input line.
Knowing which is in will let you then assume the other line from the tank is out! Then look for a line which lets water go past, rather than in, so that it goes to the outgoing line.
In other words, bypass, rather than go in, through, and out?
I tried to draw out the basic idea so you might be able to spot several valves which may need to be closed or opened at the right time.
If you are getting "some" hot water, I might guess water is going into be heated but at the same time when you turn water on at a faucet, water is also bypassing so none is staying in the heater long enough to get hot??
Let us know if that makes sense and does the trick. Lots of guessing involved, so we may need to guess again!