well the first problem isn't a problem, because it's not meant to be the reason to believe, it's meant to be reason enough to look into believing -- the "impetus" for your belief. to ignore the possibility of Christianity being the path to salvation is taking a stupidly large (and needless) gamble.

the second problem isn't a problem either, because the Bible is quite clear that all you need to do is believe in the fact that Jesus died and rose again for our sins, and accept that sacrifice.

thirdly, the Bible says that if we weren't all sinners those who didn't sin would get into heaven on their own merit, but no one is without sin.

julz