You could try to find a local dealer for parts or repair but they probably wouldn't be the cheapest option. But you're pretty fair ahead at this point already

Parts might be available online too, this is a Dolfyn? There are probably other sources, but here's Replacement Parts for Dol-fyn Distillers - FreshWaterSystems.com they have "Boiler Chamber Cord" but it looks a little different. It might not matter since they have replacement sockets available and it looks like you need to replace that too, they could probably advise you better. Obviously, seeking out qualified help like you're doing is a smart idea.

If you do get it going, when it comes to hooking it up you can probably fill it with water manually instead of attaching a cold water line to it. Mine has a line-in option and I don't use it near enough to have bothered, you might prefer it hooked up though.

If you don't get it running and it ends up being scrapped you might want to keep the lower reservoir to have rainwater in a wheeled container with a convenient tap.