Meaning of にあるとのことだった

Question

I found this sentence, of which I understand the general meaning, but can't really grasp the role and implication of the last part:

呼ばれてやってきた電気屋が調べたところ、故障の原因は室外機の基板が壊れていることにあるとのことだった

As far as I understand:

呼ばれてやってきた電気屋が調べたところ: After the technician I called checked

故障の原因室外機の基板が壊れている: The cause of the failure was the substrate of the outside unit was broken

The 「こと」 after that nominalize the sentences, like "The thing that the substrate of the outside unit was broken was the cause of the failure", but I can't understand the 「にあるとのことだった」 part; I tried searching a bit on Google, but I'm not even sure how to parse it and how the single part works together, like I don't know what the 「と」 after 「にある」 is supposed to mean.

It seems like it means something "[The technician] said that", like a formal versione of 「と言った」, and a native Japanese confirmed that it means something like that, but I wasn't really able to grasp the meaning of the whole structure.

Answer 1

If you're thinking in terms of English alone, the following might seem sufficient.

呼ばれてやってきた電気屋が調べたところ、故障の原因は室外機の基板が壊れていることにある

But not in Japanese. That's because you're explaining something. You're explaining the source of the problem. When you provide an explanation for something in Japanese, to sound natural, you make that explicitly clear by adding one of the following to the end of the explanation:

からだ

のだ

んだ

or as in this case:

ことだ

From your posted question, it seems you think that the ことにある is unnecessary. But let's look at what you would have left if you omitted that:

故障の原因は基板が壊れている

which kind of sounds like you're trying to say

"The cause/source of the problem broke the circuit board"

I suppose that could be possible. More likely, you want to say,

"The cause/source of the problem was that the circuit board was broken"

To make this clear, you need to nominalize 基板が壊れている which is achieved by adding こと. So, you could conceivably say

故障の原因は基板が壊れていることだ

But this sounds a bit abrupt. Per what I said above, since this is an explanation, it would be better to say something like

故障の原因は基板が壊れていることなのだ

However, this is clearly not what the author is trying to say. If we look at the original sentence, I would render ことにある into English as "lies in". Thus the last portion of the sentence could be rendered into English as

"The source of the problem lay in a broken circuit board"