Hi.
For the record, I agree with Clive, but I'd like to try a different analysis, just for the fun of it:
"With(out) Compaq, staying home has never been this fun."
Core sentence:
Staying home has never been this fun.
Look at two components and how they relate to the moment of speaking:
a) "has never been": present perfect. Something's in the past, but still - somehow - relevant to the present.
b) "this": Refers to the moment of speaking.
a+b) implies a disjunction between "tense" and "exophoric term 'this'" (exophoric = refering beyond the text to the real world; i.e. John? I know him. "him = endophoric." // While pointing at John: I know him. - "him" = exophoric): The "this" in "this fun" refers to the present; the "has never been" is in past, but it's being compared to present via the phrase "this fun".
Now add the condition:
"With(out) Compaq":
Do you align the phrase with the "this fun" part or with the "has never been" part?
Here, my intuition goes along with Clive:
"Without Compaq, staying at home has never been this fun," would instinctively make me align "Without Compaq" with "has never been". But I can kind of see how the newspaper editor comes up with "With Compaq," even though I don't think many people would have this as a first reaction, and it's really an editing artefact. All we have to do is find a way to align "with Compaq" with this. Let's try a change of punctuation:
"With Compaq! Staying at home has never been this fun."
Now, "with Compaq" on its own doesn't make much sense, but can somehow see it as short for something meaning "I'm at home with compaq now!" Again, I don't think that's a very natural interpretation (but people could prove me wrong). But if that's how the editor sees the sentence, then "With Compaq" would be aligned with "this", and the "this" would change from an "exophoric term" (referring to the situation) to an "endophoric term" (referring to the text); "this" would refer back to "(I'm at home) With Compaq!"
The interpretation of the whole sentence changes.
I would argue that this is a very unusual interpretation; but it could explain what the editor was thinking. (Still, the editing artefact caused by a confion about double negatives is probably more likely.)