I was listening to womens hour on the net and learned that a Jewish lady who converted from Christianity to Orthodox Judaism. Now, I believe strongly in observing the law, however, the Bible tells me that the law cannot save me from eternal damnation. Now my question is...What does Orthodox Judaism do for a person that cannot present himself perfect before a G-d that demands perfect righteousness?

"Eternal damnation" is a peculiar Christian concept- not a Jewish one. While the Torah instructs a Jew to keep all of the 613 commandments incumbent on him- he is judged on the basis of what he has succeeded in doing- both quantitatively and qualitatively (Maimonides Hilchot Teshuva ch.3). On a simple scale it is important that overall his contribution to the world was a positive one. Even beyond this, if he has observed even one commandment out of complete identification with it, he is assured of a place in the world to come by virtue of this mitzva (MaimonidesCommentary on the Mishna Makkot). This because his identity has eternal value that exceeds the mundane. On a still more absolute level- all of Israel has a place in the world to come (Mishna Sanhedrin). Gentiles who keep the seven Noachide laws- not to kill, not to steal, not to commit adultery, not to worship idols, not to eat meat removed from a live animal, not ot curse G-d, to establish courts to enforce justice- also have a place in the world to come. This when their observance is based not just on mundane social considerations but on the knowledge that this is what G-d's law, the Torah, demands of them.