Is this your first LCD with 120Hz? A lot of people who make the transition to their first 120hz/240hz TV find it awkward and unnatural. It does take a while to get used to the new motion.
However, the HDMI cable has nothing to do with anything other than transmitting the picture. Sometimes the more expensive HDMI cables might last longer, but it really doesn't matter because most people to constantly plug in and plug out their cables.
LED TV's are great and I've always preferred LCD over Plasma. However, the Quattron TV isn't very good. There is a reason why the Sharp Quattron is usually cheaper and sells at blow-out prices throughout the year. I have nothing but positive things to say about Samsung LED TVs. Pick up the D6300 or up and you'll love the picture.
If you watch a LOT of sports, live in a room that isn't very bright and watch a lot of movies, pick up a plasma. However, if you do a lot of video gaming and have kids who watch TV a lot or live in a room with lots of light, stick with the LED. If price is an issue, plasma will be cheaper.
LOL hdmi cable...
If none of the above still works, you need to pick up one of these. I'm almost 95.5% sure that this will fix all your TV problems:
Audio Quest+ 3.3' HDMI Cable