This morning I reassembled the system with the new DC-In-Board and, unfortunately, there is no change. The power supply light still does not illuminate and the system does nothing. I have tested with three different power adapters and the results are the same. I tested two of those power adapters with my 2006 MacBook and they both work fine.
The problem is definitely with the system and, given the only other part left is the system board, probably a problem with it. I checked Ebay for replacement system boards and I may as well buy a complete, working system.
For the time being I am going to consider this a completed project unless something new arises. I'll probably return to it at some point but not any time soon. Bummer as I just purchased 8GB of RAM for it right before it failed.