Ok, I was able to find a resolution to my problem without yet hearing back from Stardock. Figured I'd post here in hopes it may help someone else.
First of all, here are the contents of my sdactivate log:
Using silent activation with null serial mode.
Application start: 2012-12-31 6.1.26
Silent mode
Mode 2
Submitting activation request...
Download: failed HttpSendRequest
Result parsing error (1)
Error activating the product
Please ensure the serial number entered is associated with the email you used and attempt to activate again. Include this log file if contacting support.
In particular, note the "failed HttpSendRequest" if this is not the problem reported in your log, then this solution likely won't help you.
This post suggests that the problem seems to be SSL related and happens if you haven't used Internet Explorer to initially make an SSL connection. To be honest, I don't understand the details but the solution was simple enough: Simply use Internet Explorer and go to https://store.stardock.com.
Yeah, that's it. Whatever IE does to some Windows settings with the https request seems to do the trick. After that, I tried to start Sins:Rebellion again and this time the activation worked without a problem.
Perhaps the forum moderators should sticky this information? It might save a lot of support emails. While the solution was simple, finding the information was not.
Hope this helps. I'll put this post on the Steam forums too.