It's a Gopher Snake or Bullsnake (all in the Gopher snake family). They are harmless and nonvenomous. If you tell me what state you are in I can even give you the specific subspecies. But in any rate it is a nonvenomous and harmless snake. Their pattern does bear some resemblance to what one might find in some rattlesnakes, so they are sometimes mistaken for rattlesnakes. But it is definitely not a rattlesnake so you can tell your dad that you were right that it wasn't a rattlesnake :-).

If that's from southern Illinois then it's a Red Milk Snake. The Eastern's range is farther east into Indiana. Milk Snakes are harmless.

The snake is a Garter, exactly which species would depend on where you live, since you didn't include that information. It's harmless in any case, even if it were still alive. It's hard to say what might have killed it, but you said that you have a dog, so that would be my prime suspect, either that or a cat.

This is a Prairie Kingsnake (Lampropeltis calligaster). They are harmless, unless you are a small rodent. ;-)