Your unrelated link on a high PR site would probably stick out like a sore thumb. Look for backlinks on pages that have only a limited number of outbound links to related sites. If the page has many unrelated outbound links, then the trust factor of that page is significantly reduced. Persistence pays off. Do some research into your competitors backlink profile and contact those site owners. You would be surprised how many will actually link to you for free if you send them a personalized E-mail. Good luck
There are a lot of high PR sites that you can obtain links from for free. As stated, a nice email will work wonders as well searching around the internet can provide lots of opportunities to obtain quality, relevant links to such sites. I've blogged / written several articles revealing several such locations on one of my sites that I started in June as an experiment in Internet Marketing Strategy. (not the sites in my signature)