Ignore all the other advice, this is the part of the PCB that controls the gas valve and will be the cause of your poor hot water.
Now here is the rub, you will need a registered gas guy to fit a new one. It needs to be set up as, the ignition, ch gas rate and of course the hot water are all adjusted by settings on the PCB.
Pay attention to the solder on the pins of the cable connectors. These joints have to absorb the mechanical vibrations in the cable loom ( fan, flame turbulence etc etc ) and are going to be the first to fail. They fail with a circular crack in the solder all around the pin.I'd be checking for dry joints under the burnt areas of the PCB whilst it's out. (power = off), not that it has anything to do with the problem but because it's likely.
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