Is there reason to believe that God directly influence our lives?

Does God answer prayer, give guidance, allow for miracles, heal the sick through the priesthood, and otherwise give blessings to his followers?  To say that he does indicates that God impacts the reality that we live in.  If this is so then there should be evidence - a real, objective, effect that is measurable and testable.

With science, our understanding of truth is continually refined and improved upon.  Consider any bit of current scientific truth or knowledge: gravity, ecosystems, evolution, etc.  Scientists develop hypotheses and test against them to gather evidence that points us towards the truth.  As proofs are made and the body of evidence grows, the scientific community converges on truth and becomes united in it's understanding.

As a thought experiment, imagine a man plucked from the 15th century and dropped into today's world.  If we were to interview him about his understanding of any manner of 'truth' virtually all of his beliefs would be utterly laughable.  His knowledge of physics, medicine, and the nature of space and the universe would be eclipsed by any curious elementary school child.  But ask him about God and religion, and his belief would fit right into the spectrum of belief today.

This is because there is no way to test against the claims of religion or gather evidence to prove, or definitively refute it.  Where our knowledge of science, technology, and medicine has evolved and improved dramatically, our knowledge regarding the truth of religion has not budged.  And unlike within the scientific community, religious communities fracture and splinter.  New sects and ideologies are sprouting up everywhere.

To me, this lack of convergence strongly indicates that fact-based empirical evidence does not exist in religion.
  

I've laid out this argument in this past and been rebuffed by believers with the idea that God demands faith.  The argument goes that evidence would preclude the need for faith, and faith leads us to truth that is beyond understanding or immeasurable/not testable.

If we accept the argument that God's influence isn’t testable or measurable then our 'evidence' for belief is no longer empirical.  It is internal and based on personal feelings and emotion, or individual anecdotes (attributing our circumstances to God). 

However, given that people of all faiths describe similar emotional conviction as rationale for their beliefs, how can one truly know that his or her faith is correct unless one gives a thorough and fair investigation of other systems of beliefs?

But this would require a mind clear of bias - the clarity to recognize and stamp out internal cognitive dissonance for what he or she was raised to believe.  This is not simple, and may not even be possible.

Only by making a concerted effort to do this, can one defend his or her system of belief as the correct system of belief.

Still, this only applies to individual because this process is based on personal reaction to these doctrines and faiths, and not based on measurable, statistical evidence.  I can't find justification to say that this leads to perfect truth, only that it leads to the faith that is most meaningful to the individual.