It's almost unbelievable to me but virtually everyone is giving you bad advice. If your TV is a HD set and it has a coaxial connector on the back to hook up your antenna, then it has a digital tuner and as the only other person giving you semi-good advice says, "you are good to go".
Now, as to exactly what is going on and why you are having the problems you are having, lets work on that a bit.
You say "I do see a very snowy channel that says "CBS-HD" on the bottom right of the video". Because you say it is snowy, that tells me that you are really not tuned to a digital channel.
Digital channels do not have snow. They may freeze or pixelate... but they will not have snow.
Right now, just about all stations are multi-casting. That is, they are broadcasting both analog and digital signals. I've never worked in the TV industry but I presume your local CBS station is putting the CBS-HD logo on screen to advertise they have HD... and I would certainly agree that this could be a source of confusion.
Recheck that CBS station and then come back and tell us what the channel number is. Digital stations will all have channel numbers like 12-1 (or 12.1) whereas the analog station will probably have a number of 12.
The comments you have made about your indoor antenna are confusing to me. You say it is indoor... but then you say it has a motor to adjust the direction. I can not think of a reason an indoor antenna needs a motor... so I'm wondering if you have made a mistake here?
Also, can you go back into AntennaWeb.org and then tell us how far away those 5 or 6 digital stations are?
An indoor antenna works ok for relatively short distances of maybe 20 to 35 miles or so, but any further than that, you will probably have problems.
The last thing which comes to mind is that you say you have just bought this HD antenna... I don't know how you got your TV signal before, but since you have just hooked up your antenna, you need to go back into your TVs menu where ever the channel scan function is and rescan.
My experience with Radio Shack is not good. If you look at the reviews, you will see several good ones followed by a couple really bad ones. The simple fact is, you may well have gotten one of the bad ones. The distances you are saying you are from stations is close enough that rabbit ears should work and give you a decent signal.Traffic stats