Jim, you've done an incredible job weeding through all the irrelevant info in this thread which should have only been 2 posts long:
1) Do I need a splitter?
2) No, you need a switch.
Buy your Trendnet switch. It will come with a power supply to plug into the wall. You'll also need a short ethernet cable for each of the devices you intend to plug into the switch. If you don't have these already, I recommend buying those at monoprice.com. Amazon may have cheap ones as well.