Ah, I see...
Like you say, 2nd hand, out of warranty... time has been spent, for someone who is not actually a customer... salaries have to be paid, etc, etc...
But I agree, you really should have been aware of inspection charges upfront. Any idea whether they would have charged a fee if the engineer's diagnosis was "it's fried, not worth fixing" (it's conceivable their quote for fixing was actually along those lines??)
I sense that, in hindsight, you can see their point slightly - but the point is, if they'd said upfront "Yeah send it in, we'll charge you X an hour to diagnose it" then you might well have not bothered...
Assuming they have it, and you don't want/need it back now, I'm with you, don't pay it - ball's in their court... see what sort of fuss they want to make, then make a fuss back about their lack of communication.