Static Sound along with Static/Jumping Picture.

the static sound may be due to a defect in the high voltage circuits, IE Fly-back transformer or and voltage multiplier, posibly high voltage leads to the CRTs arching to ground, finally horizontal sweep circuits

The set isn't fully tuned into the channel the satellite receiver is outputting on (should be channel 3 or 4). If this set is old enough it may have a fine tuning adjustment that needs to be tweaked a little to clear up the problem. Some Zenith TV's also had a switch to select different tuning systems. If set incorrectly this might happen. If yours has such a switch, make sure it's set to "normal" or "air". It may also be that just due to age the turner isn't working properly.

It might be time to consider replacing that set. A new one would give you all the picture and sound quality your satellite can give you. Right now you're paying for quality you can't appreciate.

try cleaning ALL the contacts involved with Caig DeOxit (D5, S5. F6, G5, etc.) products*, they work very well. e.g.; cables, inputs, outputs, and (if you're confident) all the contact points "under the hood". this static you speak of sounds like less than stellar contact points and can addressed at home if you've the motivation to DIY.
* amazon.com/D5S6-Contact-Cleaner-F5S-H6-FaderLube/dp/B00HNV7WI2?SubscriptionId=AKIAILSHYYTFIVPWUY6Q&tag=duckduckgo-d-20&linkCode=xm2&camp=2025&creative=165953&creativeASIN=B00HNV7WI2

Sometimes you just have to shoot the old girl.

If this jumping is accompanied by a sharp snapping sound, it may be the high voltage circuit discharging to chassis. Leakage can cause the jumping and a discharge can momentarily blank the picture.

If you want to try a 'cleaning cure,' I suggest you pull the plug (not just turn it off) for several hours, preferably overnight. Sets of this size can carry enough static charge to punch a hole through your thumb if you get careless.
Remove the rear housing (shouldn't be more than 6-8 screws) and using a clean paintbrush, and possibly a vacuum to **** up the dust, clean it well and pay special attention to the area around a largish misshapen black plastic object bigger than most anything else and connected to the back of the picture tube via a fairly thick cable.     

volume control has been complaint may be...

Ionic Breeze is no longer supported because Sharper Image went into bankruptcy as a result of these products proving to be ineffective.

Here is a Sharper Image article

Here is an EPA article

Use your warranty, as most warranties are vioded if you open the set up.

How old is this TV?
Sounds like it has high voltage failure.
(If you hold your hand on the screen when you try and turn it on, do you feel the static? )
Unless the set is over 10 years old, I would overhaul the high voltage circuit. Should cost under $200 at a shop.
Hope ya fix it!

If it is under warranty, you would be better off the return it for an exchange as the main board will need to be replaced. this board is not cheap. Good Luck