What is more shocking than the burnt out wire on the left is the yellow and green wire on the right. That wire is the ground wire. It is supposed to be connected to the body of the boiler. It is not. If you look closer you can also see a bolt missing that is meant to hold tight another wire meant to ground the heating element. It is there to protect human life. If G-d forbid there is an electrical leak somewhere the escaping current is meant to run through that wire to the ground. If it is not connected and there is a leak and someone touches that boiler...yup, not good news for whoever touches it...Sadly many boilers we service are not grounded.
There are several factors that affect the efficacy of your boiler to produce hot water for you.
Sometimes the problem lies at the thermostat. It may have to be replaced or reset. Perhaps the boiler is leaking water onto the wires and created a short. Then, when you try to turn on your boiler, you end up shutting off the power in the entire house.
Other times there is a build up of mineral deposit in your boiler. Instead of the heating element (a piece of metal inside of your boiler that heats up and heats the surrounding water) heating the water you are heating all the minerals that have deposited themselves all around the heating element. You end up heating them and not the water. It may take two hours until you have enough water to take a shower.
If you are not receiving hot water from the solar panels:
Sometimes the panels are not installed properly and an air bubble becomes trapped in the pipes preventing proper thermosiphoning. That means that the hot water will stay in the panels without making their way into the boiler. And that means no hot water for you!
Or, everything may be positioned correctly but either the air release valve is faulty or one was not installed.
Older panels may have to be flushed out (from rust build-up) or replaced if the pipes that comprise the panels rust through.
All the best!