I think the internet has had a somewhat marginal but noticeable effect ( it certainly helped me find the information I needed to get out ) but I don't think it is a massive factor. The idea that the explosion of information has led to people being far more informed and making much wiser decisions based on greater knowledge simply isn't true ( see the election of Donald Trump as an obvious example. )
In many respects , it has led to people polarising their views - seeking out information that backs up and confirms rather than challenges their world view. I know a few JWs who only regard JW.ORG as the only website they look at. Many in my old congregation refused to watch the Panorama program on JW child abuse - similarly many immediately mentally or physically switch off when they hear or see anything online that might be "negative".
The reduction in the growth of JWs has many factors. Part of it is based on the law of diminishing returns - it is very difficult to grow a business ( which essentially is what the Society is ) consistently year-on-year at the 4% - 5% per year growth rates of the 1960s - 1980s ( pre & post 75 exponential growth & fall excluded ) Part of it is simply that in the West , especially Europe , people have very little interest in religion any longer and most religions are in long term decline , including JWs.
There is still some growth in 3rd world countries , much of it from people moving away from established religions , but even here JWs are competing against Mormons & Evangelicals for the kind of people who are attracted to these new religions. http://www.economist.com/node/21551091 Many of these competing religions are much more attractive than JWs - lets face it , life as a JW is pretty boring and unfulfilling and requires a commitment in terms of effort ( eg the ministry ) and sacrifice that many other religions don't require.
All told - I would think that the direct impact of the internet is probably in the area of about 0.5% to 1% drop of growth every year in terms of existing JWs doing research & leaving and contacted persons doing research and not continuing their interest.