In a slightly earlier period, we do have evidence of the prostitution of barely pubescent children in London, for instance, though these children were generally over the legal age of consent (which was raised to 13 in 1875, I think). The Cleveland Street Scandal (which started with a 15 year old boy) and the Elizabeth Armstrong case (where a newspaperman was able to purchased a 13-year year old girl for £5) are two of the more famous scandals arising from the practice (both acts were still very illegal, despite the age of consent). Cleveland Street was a "rich and powerful ring", but I would guess most of the child prostitution in this era was not catering to the rich and powerful--though obviously being rich and powerful grants easier access to most things that money can buy, and does a great deal to shield one from the consequences.

Many of the more recent accusations of pedophile rings (but certainly not all of them) have proven to be shams. "Satanic ritual abuse" accusations were relatively common in the 1980's in America. The two main events that precipidated this were the "recovered memories" "memoir", Michelle Remembers, and the McMartin Preschool scandal. Read particularly about McMartin. One of these was the alleged "Franklin County, NE child prostitution ring", which was alleged to include powerful members of the Nebraska Republican party, but the accusations were ultimately found baseless (and at least on the accusers indicted for perjury). One of the last big cases was the West Memphis Three (convicted in 1994), who were recently exonerated. I do not think a single case of Satanic ritual abuse has ever been demonstrated in America. It was a pretty typical moral panic (and indeed, I first heard about it while studying moral panics), and intimately related to the wider "day-care sex abuse" scandal. I can think of no example of an instance where pedophiles were "really pulling strings" in the period you're asking about, though there are many examples of individuals abusing their office to take advantage. In 1983, two members of congress were found to have had inappropriate sexual relationships with 17-year old pages. Again, though, we're more likely to see powerful individuals than powerful rings.

Now, this is not to say that there is no pedophilia, no institutional participation in pedophilia, and no organized groups of pedophiles. Indeed, I believe that some of the daycare cases were legitimate cases despite being part of the moral panic. The victimization rate for child sexual abuse is something like 1/5-1/7 girls and 1/20-1/25 boys. In his famous 1953 study, Kinsey found a roughly similar overall rate (though I think he found a rate for boys that was higher--I can't remember). I just came across a little piece called "Placing Childhood Abuse in Historical Perspective" from one of my favorite social scientific blogs, by the historian of childhood Stephen Mintz. It may interest you, but there's no mention of powerful organizations or anything of the like, though, like today, there was likely the fear of them (see the Mann Act and the general moral panic over White Slavery)--likely, it's easier than recognizing the reality that up to half of all sexual abuse of children is carried out by a member of the victim's extended family, and most of the rest is carried out by another acquaintance of the victim.

In Belgium Mark Dutroux kidnapped, sexually abused and killed many young girls in the 1980s and 1990s. Dutroux claimed he was part of a very powerful pedophile ring. There's some circumstantial support for it.

As the Guardian article says :

"Dutroux himself said ... "A network with all kinds of criminal activities really does exist," ... "But the authorities don't want to look into it." And there is no doubting that things do look odd.

The original investigating magistrate was dismissed after sharing a meal with one of the victim's families and several prosecutors, policemen and crucial witness have committed suicide. Important evidence has also disappeared."

Public perceptions of corruption and incompetence eventually led to 300,000 people marching on Brussels in protest.

I think there is some credibility to the claim Mark Dutroux was connected to a powerful pedophile ring, with influence over the criminal justice system, in the 1980s and 1990s in Belgium.

Sources

http://www.theguardian.com/world/2002/jan/25/worlddispatch.dutroux

The Wood Royal Commission in New South Wales (Australia) investigated allegations that there was a network of prominent/powerful paedophiles being protected by the police back in the 1980s.

The conclusion they came to was that there were paedophile rings (reference was made for example to the Paedophile Support Group and BLAZE) but that they were not the all powerful groups claimed initially. Corrupt police had interacted with members of these paedophile rings, but the relationship was actually built on the paedophiles paying the police bribes/being extorted by Police, rather than the police being actually involved in the rings 'main' activities. The report emphasised that the paedophiles were vulnerable to pressure from corrupt police because of their activities, in contrast to the 'all powerful' thing.

As a result of these bribes paedophiles may have been warned about investigations etc. but again this doesn't necessarily support the all powerful ring idea - for the corrupt cops this was probably just a question of protecting their 'revenue'.

Now, we might assume the report could have suppressed information about high profile paedophiles precisely because they were so powerful. But given the enormous impact the commission ended up having on the NSW police (and by association the government) which led to a big shake up it seems pretty unlikely that some shadowy network of high ranked paedophiles got away with it.

You can read the whole chapter of the commission report devoted to the topic here:

http://www.pic.nsw.gov.au/files/reports/RCPS%20Report%20Volume%204.pdf

It covers a lot of other material like failures in the investigation of sex offences etc. though so it is pretty long (367 pages).