You are really stretching there Kevin. Demonstrating that a claim like the earth is only 7,000 years old according to the Bible is false does not disprove the Bible, because the claim itself is suspect and may not be what the Bible teaches.
We're not talking about that easy straw man example for you to knock over, now are we.
What about Mormonism's long standing claim that Indians = Lamanites = Israelites? Science has disproved this rather easily. This means, quite simply, that not only has the Church been wrong about this point, but that it shatters a fundamental truth claim of the Church. For if Israelites never colonized the Americas, then the Book of Mormon story is bogus, and then so must be Joseph Smith, and the Church falls along with them.
There may be a number of reasons the claim may be false (or demonstrably false) which has nothing to do with the inspired nature of the text itself, but in reality can be attributed to a poor interpretation or limitation in understanding of the men who wrote the text itself.
Oh, so you think it is a good idea to say Joseph Smith, the founding prophet of the "Restoration", wasn't in a good position to properly interpret his own scripture?
How in the hell does this help your case? If we can't trust LDS prophets to interpret their own "revealed" scriptures, then why should we trust them on anything else? You know, like properly interpreting the Bible?
In any event, your claim that science cannot disprove religious claims is demonstrably false, and idiotic. Of course it can. It does it all the time.
But my favorite example of science disproving a religious claim is how the science of Egyptology disproved Joseph Smith's claim to have been able to translate Egyptian documents. The only reason he ever made this claim was because he knew no one was in a position to disprove him at the time.