Would you say:
There is no fire or hot ashes in the fireplace.
or
There are no fire or hot ashes in the fireplace.
And where does that question mark go?
Would you say:
There is no fire or hot ashes in the fireplace.
or
There are no fire or hot ashes in the fireplace.
And where does that question mark go?
"There's no fire or hot ashes in the fireplace."
Neither "is" nor "are" sounds right. With "there's", you avoid the issue, since many accept that with a plural subject.
Another possibility is:
There is no fire, or hot ashes either, in the fireplace.
This avoids the problem, because the main verb does not agree with something within a parenthetical expression or aside.