Thank you for your replies, guys. Some interesting ideas here.
As far as uniqueness of the page on my site (except for title and the question) - I am pretty sure about it because in this particular example I was the only one answering and none of the answers were copied from anywhere. When other users are also answering, indyank is right, I cannot be 100% sure the answers are not also copy/pasted just like the question was. However, it stands to reason that even in that case the answers would be copied from different places on the Net and the resulting page on my site would still be different from the one that Google chose to show instead of mine.
@Simsi: I could have linked to the other page, but the funny thing is: the person asking the question has completely switched to using my site and he has posted more information about his issues and even posted some pictures that were not available to the people answering him on the other page. So, other than "Google gaming" there really is no reason to link to that other page: mine has more info both on the asking and on the answering side. That's what irks me here: even the original poster has completely switched to using my page (I don't believe he's even been back to that other forum page) and yet Google still gives the preference to the page that was posted about 48 hours earlier, has the same title and the same first couple paragraphs.
@ascensions: what would you parse/replace? I can think of adding something to the title (I've already added more than enough to the content) although I'm not sure what would be best to add here. However, I can't think of replacing anything without making this look really-really weird. It's a very simple title, too. He just typed "Need help with a broken XX-XX-01". Not much room for change...