Ok, the first thing that sticks out is you say "non powered" and this is a powered unit. First thing I'd say is dig out the power inserter and install it.
If it IS powered, there are better splitters you can buy that only have around 3.5db loss per side or you can work with a tap splitter and hook the card to the low-loss leg.
At 40 feet, you're losing another 4 or 5 db depending on the cable. You could try an amp right where the splitter is to overcome the length.
Lastly, look at a more standard antenna. Just looking at that one, I'd say it's not going to do well if you're more than 15 - 20 miles from the transmitters. It appears to be omnidirectional, so it's more prone to multipath issues.
Seriously, I'd try to get more or a better signal coming into the house if it all possible. Standard antenna with a pre-amp may be the way to go.
Check your location at www.tvfool.com
and, if you like, start a thread in HDTV Techinical. Or read the OTA FAQ and a few other threads in that section. We're all antenna geeks over there.