Looking back, one turning point in my life was the day when a dear friend of mine told me: "I never understood why Jesus had to die for us."
We were two Bethelites sitting in the (French) Bethel library. She was the daughter of a DO, "born into the truth," etc. Startled, I went through all the WT demonstration, feeling increasingly stupid as she kept smiling gently. No this didn't add up.
This was the start of a great series of incredibly free and illuminating conversations, opening a completely fresh reading of the Bible to me. Coincidentally, I had to translate the article "ransom" for the Aid book shortly afterwards, and successfully pleaded to entitle it "rançon, rédemption" ("ransom, redemption") as the notion of "ransom" was definitely too narrow, even for the actual contents of the article.
As Leolaia pointed out, the notion of "ransom" is just one of the many interpretative patterns applied to Jesus' death (and resurrection) in the NT (I posted an analytical table to some of them in http://www.jehovahs-witness.com/9/90444/1517804/post.ashx#1517804). There it is far from central, far from systematic, and nowhere related to Adam's sin. As RodP said (unfortunately I didn't find the corresponding article) it is entirely distinct from the sacrificial notion of expiation (which is not central either). It is not a classical doctrine in later Christianity (cf. saint Anselm's Cur deus homo?, "Why did God become a man," which offers a completely different explanation for Christ's incarnation and death). Only in late 19th-century adventism does the notion of "ransom" actually come to the fore -- if not only in Russell's group, this would be an interesting issue to search.