This isn't really an answer, but maybe it will help. I found that the Source is included in the International Index to Music Periodicals, an online database to which many university libraries subscribe. However, the actual text of the articles with the "Power 30" lists are not included. However, it might be possible to get the articles from your local library's Interlibrary Loan service. I can give you the citations for the issues and page numbers of the relevant issues if that would be helpful.
Here is one partial affirmative answer: Jay-Z topped the list in 2009. See http://power30.thesource.com/.
Some additional information
Here are some other thoughts:
1. You might try simply calling the folks at the Source. They would likely have that answer for you fairly quickly, if you could get someone from their research department on the phone. I'd ask for "research" or "the library" when calling them at (212) 253-3700. You might also try emailing their media office at press@thesource.com.
2. I can't find any libraries in the area that have full print runs of this journal. The most substantive collections are at the Schomburg Center and the Library for the Performing Arts, both parts of NYPL. Here's a link to the catalog record from NYPL: http://catalog.nypl.org/record=b11870642~S1. Between the two libraries, you should be able to browse most of these issues.
It also looks like the journal hasn't been available by subscription since 2006, which appears to limit how much these libraries are collecting the journal. I suspect you'll have the best luck contacting the magazine itself.
I hope this is helpful!