Re: Why hoping and not to hope
Welcome to Using English.
THANK YOU for Giving your thread a good title, using proper capitalization, and using proper punctuation.
"Hoping" describes them, when they called in the electrician. They were hoping he could do something, and in that state of hopefulness, they called him.
You can't use "to hope" to describe them as they made that call.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.