plmkrzy,
I would like to attempt to tie together some of the bits of information you have already received on baptism. I'm not trying to tell you what to believe, or what you should do about the situation.
Historically, there are two Christian views on baptism. One is the sacramental view, and willy-think did a very good job of quoting from the early Church Fathers to expound this view. It really is the older view. It is the belief that the gift of the Holy Spirit, given through baptism, imparts to one God's grace (which is here conceived as an actual power). Of course, if the Spirit is transmitted in such a physical way, then this must occur within a succession of persons who are authorized to perform the baptismal rite. This view of baptism as a sacrament is maintained by the Roman Catholic and Eastern Orthodox Churches, as they claim to have a succession going all the way back to the apostles who were authorized by Christ to perform baptisms.
The second historical view comes to us through the Protestant Reformation. Protestantism claims that our relationship to God through Jesus Christ is initiated through our faith in Jesus, not through any physical action performed upon us by a priest or minister. This creates a need for another explanation for baptism, and it is this: That baptism, being a picture of death and resurrection (if performed by immersion), merely symbolizes something that has already occurred in the life of the believer.
Where does the Watchtower Society fit into this picture? The fact is that Charles Russell inherited his understanding of baptism from Protestantism, so that JWs still claim that it is a symbol of dedication. Russell thought that he was engaged in "harvest work" - that people in the churches who were already anointed Christians were being called out of "Babylon" to associate with the Bible Students. If these people were already "consecrated" or dedicated to God, their baptisms were valid and there was no need for them to be rebaptized. Fred Franz came into the movement at the time when this understanding was still current, and as badwillie has told us, was not rebaptized.
After Russell's death, Rutherford began emphasizing that JW's were exclusively "God's organization." They were no longer a movement or a loose association, but a concrete organization that competed with the churches. But even Rutherford, toward the close of his life, wrote a book entitled "Children" in which he tells the fictional story of a young couple who learn "the truth" and are baptized by one of their non-JW fathers! So it remained for the Knorr-Franz team to set a policy of not accepting outside baptisms (and when this occurred I don't know, maybe someone else does). The Society has never explained just when outside baptisms became invalid, but if they had to give an explanation I wouln't be surprised if they said the cutoff date was 1919, because that's when they think that Babylon the Great fell.
By refusing to accept non-JW baptisms today, the WT is in effect making baptism a sacrament (that is, the view that the Spirit is only conveyed through a certain physical channel) even though it claims to hold a symbolic view of baptism. If baptism is merely a symbol, it does not matter who performs it as long as the one being baptized has undergone a change of heart. Furthermore, the Society has no authority to perform sacramental baptisms because it cannot trace its succession back to the apostles. To have sacramental baptism, we need more than just a few "wheat" scattered among the "weeds" for the past 1,900 years!
I hope this explains how the WT got into the ridiculous position it is in.
Justin