By "clear signal" do you mean a high def image or a picture without any intereference? Two totally different things.
What I'd try is this:
Your new TV (great deal btw) probably has hdmi, component and s video inputs. Your receiver probably has the same outputs. Hook each up and then select from the tv's menu the various input sources and see which one gives you the best or clearest image. For eg: hdmi on video 1, component on Video 2 and s video on 3. (you should get the best image via HDMI).
If you're noticing interference or snow, you might want to see where your cables are being run. Having one in direct contact or proximity to a heavy magnetic field might give you snow. I know many are supposed to be shielded, but a strong mag field can cause problems.
One thing that drives me nuts is with the component video connections, each connector isn't labelled very clearly. I know, they're blue green and red but for a guy that's blue/green colour blind, whenever I connect this setup I have a bitch of a time....(trial and error).
Oh yeah, if your DVD player isn't high def, or upconverting, an HDMI cable won't work on it so you're stuck with low or med res (780 I think it is). If your sat receiver isn't HD compatible, you're screwed lol. You'll still get a nice picture, but not HD and believe me, HD is life changing. Not to sound like a pussy or anything but sometimes when I watch PBS (the best HD programs I've found to date) I often get a little mesmerized just by the quality of the image, not the content...
Not to get too far off topic, but when I first got HD I was friggen amazed to see that during a leaf's game, and they had those shots of the guys on the bench, you could actually see the little diamond shaped holes in the athletic knit jerseys on the players.....(the downside is you also get to see Cameron Diaz's bad complexion among other things like shitty makeup and I saw a funny thing recently: after a passionate kiss, the heroine in a movie had her lipstick smudged all over her bottom lip and you could see it plain as day on HD lol)