For what it's worth I think that if you want a substantial amount of someone's professional expertise you need to offer something in exchange for it. It's one thing to ask for a quick favor from someone you know but another thing entirely to expect them to spend extended time on something, especially if you just drop it on them when they didn't expect it.
If someone asks me if I'd be free to look at their laptop I can consider what's required, when I might have time and indeed whether I want to take on the responsibility for it at all. If someone invites me round for dinner and then suddenly drops a detailed technical problem on me, expecting me to spend a substantial time out of what I'd expected to be a social evening, I'd take a pretty dim view of it. It seems to me that it's a pretty basic courtesy to add the request to the invite, even if it is in the form of "Hey, are you free for dinner on Wednesday? It would be great to see you. If it's an easy enough fix would you mind taking a look at my laptop while you're here?" - at least that way everything is on the table and we all know where we stand.
