Logic problem: The founding principles of the U.S. and Christianity.

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Here's what I think:

Many Christians promote the belief that the U.S. was founded as a Christian nation.

I agree with them.
Why? Well, the majority of the population of the US was indeed christian.

However, I'm sure that they cannot contradict the your constitution that explicitely states that the congress cannot make laws that favor one religion over the other. And now, especially when America has large populations of non-christians(I'm excluding atheists, since most atheists are of christian upbringings or *culturally* christian).

As some of their evidence they say that the founding fathers were Christians, and that the country was founded on Christian principles (for more see the video link).

It certainly does not matter. If the founding fathers were, say Jews, would America be a Jewish nation? It certainly would still have been a christian nation no matter what, since the majority of the people and the people who voted for the leaders were, in fact, christian.

Aren't ideas like freedom of religion and the separation of church and state naturally opposed to what seems to naturally become the Christian agenda

If you want to discuss theology...We can, of course. For example, I can quote stuff from the bible that seems to support a secular way of life, meaning, seperating the state from the church, some will agree, some will disagree, and most of you probably know what I'd quote from the Bible if I'd quote it.

My idea is, if the founding principles of the US were opposed to the Christian religion, I could state from the start that people would certainly not be very accepting of them in the first place.

that is to dominate, oppress, and take over

Overdramatizing again, are you?

If the founding father's really were Christians bent on making this a Christian country why would they want freedom of religion and a separation of church and state?

Let's see. Maybe they saw how the anglicans and catholics were always hitting eachother over the head back in England(the country they originated from), and stated that religious(denominational) conflicts would not rule the US? And America was alsor receiving large quantities of puritans that fled persecution back in Europe. The promises of freedom of religion promised them this.
Besides, it was as a matter of fact, a Christian country back then. People were much more religious, and religion played a large part in people's lives, not to mention that the majority of the population was as a matter of fact, Christian.

If we in the U.S. were to go back to our Christian roots so to speak won't that involve trashing freedom of religion and the idea of separation of church and state?

I don't think so.

"That the separation of church and state does not exist in the constitution"

It certainly does.
Besides, what does the state do? It enacts laws. And this is where the first amendment really hits it.
It's fairly certain to say that secularism is guaranteed by the State.
However, it does not have an anti-religious, or an anti-christian stance.