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The wires should not show heat damage. The reason this occurs is because the board terminals are not making a good connection with the wire harness terminals so over time the wires heat up and likely the cause of your original problem. Without replacing the wires as well as the board you replaced, the issue will likely come back but there is no telling how long that could be.
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So the only blackened wires I see are from the fuse wires. If you buy a new fuse it should come with new wiring and if you're handy you can replace it yourself. You'll need the full model number but you can order it from Repairclinic.com if you wanted.
You would need to replace the wire harness then and that is not something easy to replace since it runs all the way through the door down below the dishwasher. You'd need to call a part store to look up the part number if you wanted to try to replace it yourself but I think you'll need a technician.