For example, in the logical case where it is true that God exists and it is false that the Bible speaks the truth, the implication mentioned in premise (p1) is false. That is, the implication "the fact that God exists implies that the Bible speaks the truth" is false. This in turn makes the premise itself false since the premise is a conjunction of two terms, one being the implication in question.
Also, for each particular logical case, such as the one you mention, each basic term has the same truth value in both premises and in the conclusion. That is, for a particular case, if "God exists" is true in the premise, it is true as well in the conclusion.
However, how this play out depends on each particular argument.
It wouldn't be valid even in a situation where you would know that the premises are true since validity doesn't depend on whether the premises are actually true.
I don't see how that could help, but that's all I can do.