Links that you've built to your site will still point to your URL, and will count. Unless you are looking at a scenario in which a person linked to you solely because he thought your home page looked good, and removed the link just after the template change
I wouldnt think it should do very much just changing the template. Especially if all the information and links still exist.
It won't have any affect on your backlinks. However, it may have an impact on your ranking in search engines.
Check the question again, he said that urls will be the same, only template will be changed. If urls are the same, then PR will not be hurt, however, there could be some flux in the rankings due to content update in new template...
As long as the webpages remain named the same there is not relationship between design and backlinks. Unless you have a large number of people linking to your graphics that is.... but that is another issue.
I really don't know, what exactly you had made with your website. But in general, if you are just updating your design, you will not loose your PR. There might be some flux in rankings due to change in prominence and density of website content..