Where does it say Sparda is dead? I just thought he had disappeared.
Let's see.
Sparda sealed off demon world to protect humans. He then found a human who he fell in love with.
That human gave birth to two baby demons.
Later that human died and the two baby escaped somehow.
Then in DMC 3: Arkham goes and plans to open demon world to get Sparda's power. Vergil also wanted to do this too. Later in DMC 3 Vergil goes into demon world.
And in DMC 4 people try to open demon world again.
If Sparda has been alive all this time then he's one big of a bastard. Not being there to protect his sons and wife, the humans by keeping demons at bay.
Common sense
I wonder how he died though? Must been a side effect of him being without his powers.