[JRTJH]

That "single valve" is turned to the bypass position. The way the valve is set, it sends the cold water up that blue PEX tube and into the hot water lines (red PEX tube), effectively bypassing the water heater.

The valve is a 1/4 turn valve. Turn it so it is "in line with the lower water heater inlet port and then water will be run through your water heater.

The PROBLEM I think you may have, if as you say, the water heater is "hot" when you touch it, is that you may have turned it on with the water heater tank empty. That could destroy the electric heating element and if only using gas, could "superheat" the tank, buckling it and causing a leak or possible future corrosion.

About all you can do at this point is turn the bypass valve to "the operate position" and fill the water tank with water and see what happens...

DO NOT FILL IT WITH COLD WATER WHILE THE WATER HEATER IS HOT TO THE TOUCH..... Turn the water heater off and wait until it cools so you don't split the tank by filling it with cold water while it's hot.....