What resolution is your satellite delivering to your TV set? 480i or 480P? Or is it 720P or 1080i which delivers the sharp pictures to your TV set?
How about any other boxes connected to your TV?
Also the TRUE source of video has an effect on it too. If you're watching DVDs instead of Blu Ray DVDs you'll see a sharpness difference and a Satellite TV channel that isn't their HD channel will only deliver a picture in 480i (SD) resolution.
I have both settings on my cable box, and even some of the older Pre-2006 shows are SD shows.
If your pictures are grainy, that's usually the reasons why you have a grainy picture.
Satellite box not set to 1080i, Connections -- cable connection is the old Yellow Red White connectors or the TV tuner set to channel 3 (SD) input.
It should be the HDMI or the 5 wire Component cables and the box's Video out set to 1080i.
The TV stations -- You should see HD listed in the TV channel's name box. And the TV show should have a listing of HD in the Information box for that show.
If you find all of that is correct...then you may actually have a problem with the TV set.
If you have the TV's remote available to you, I find out if the Display button shows 480 in the TV's display box. On your ORIGINAL TV remote....there's an INFO button at the 4 o'clock position right by the Ok and arrow rings.
When you press it, it should list the Satellite or DVD signal resolution it recieves.
All grainy pictures come from the source, not the TV itself.
That's why we want to make sure the source is delivering 1080i first, the shows are HD shows and the TV station is also listed as an HD station, before we assume the Video board or logic board is broken.