Plugs are not much less than a whole new cord. Kind of sucks. But if you cut off the old cord plug the new one will be better, assuming you get it on right.
You might have not twisted the plug on fully to the recepticle. The 30 amp twist lock is a very bad design. It's easy to not make a good contact. You should make double shure you are prolerly twisted on and then use the locking ring to secure it.
You might also need to replace the boat plug. It's rare to burn one side and not the other.