The Trinitarian idea is that Jesus has two natures both God and man. And it would be absurd to say that God died. After all we are explicitly told that God only has immortality (deathlessness). Therefore it could only be Jesus' other nature, the nature of man, that died.
The Trinitarian claim is that the son of God is eternally begotton(contradiction) meaning that there never was a time that he was not. The son of God is a member of the Trinity and therefore can not die.
So how is it that God gave His own son to die on the cross(Rom 8:32) if the son cannot die because he is eternally God and the second person of trinity?
No.
If God died then there was no one left to raise God from the dead.
Psalm 6:5
Ecclesiastes 9:4-6
4 For to him that is joined to all the living there is hope: for a living dog is better than a dead lion.
5 For the living know that they shall die: but the dead know not any thing, neither have they any more a reward; for the memory of them is forgotten.
6 Also their love, and their hatred, and their envy, is now perished; neither have they any more a portion for ever in any thing that is done under the sun.
If God died then then scripture is wrong. For there are many scriptures that clearly state that God raised Jesus from the dead.
Thus establishing the point that if God is dead, then there is no one left to raise Jesus from the dead.
If Jesus has not been raised because there is no God alive to raise him
I Corinthians 15
Now if Christ be preached that he rose from the dead, how say some among you that there is no resurrection of the dead?
13 But if there be no resurrection of the dead, then is Christ not risen:
14 And if Christ be not risen, then is our preaching vain, and your faith is also vain.
15 Yea, and we are found false witnesses of God; because we have testified of God that he raised up Christ: whom he raised not up, if so be that the dead rise not.
16 For if the dead rise not, then is not Christ raised:
17 And if Christ be not raised, your faith is vain; ye are yet in your sins.