The "inerrancy of the Bible" is not only based on faith but on the authority of eyewitness accounts, fulfilled prophecies, and historical fact.
With respect to Noah, these are the words of Jesus Christ:
"But as the days of Noe were, so shall also the coming of the Son of man be ~ Matthew 24:37 (KJV)
He also mentioned Abel, another pre-Flood historical person:
"From the blood of Abel unto the blood of Zacharias which perished between the altar and the temple: verily I say unto you, It shall be required of this generation." ~ Luke 11:50,51 (KJV)
The Hindu vedas? You mean their "Good Book" of writings which teach multiple deities? Who are their eyewitnesses to their teachings? Can Hinduism back up any of its prophecies? From what authority do they speak?
Your argument that neither the historical account of Judeo-Christian Bible or Hindu Vedas can be validated or discredited depends on which "truth" and eternity you seek.
It's based on the Revelation at Sinai. No eyewitness is necessary to believe G-d always speaks Truth, "historical facts" are often denied, and whether or not a prophecy has been "fulfilled" is often a matter of personal opinion, prejudice, or logical fallacies such as affirmation of the consequent.
Sinai proves everything.
And those eyewitnesses are documented where? Also the prophecies? Historically there is evidence supporting the life of Jesus and most of the people in the New Testament - but does that prove the divinity of Jesus?
Proof has an extraordinarily high level to achieve. If you cannot achieve it, then there is a level of faith required. That's the point - religion cannot be proven, but it does not need to be proven because it is FAITH.
Your argument that neither the historical account of Judeo-Christian Bible or Hindu Vedas can be validated or discredited depends on which "truth" and eternity you seek.
That's the thing about faith - you have to choose which truth you want to believe in. And which eternity you want to seek (which in itself is a concept that has yet to be empirically proven).