34 years refers to the time since British troops were sent to Northern Ireland following a plea from Gerry Fitt to protect the Roman Catholic minority, who were suffering from an almost apartheid-style discrimination at the hands of the majority Protestant population. Growing up a Catholic in Northern Ireland was to be largely condemned to second-class citizenship (I have a large chunk of my very Catholic family in Northern Ireland, so I do know what I'm talking about).
As to why things went sour - that's another can of worms altogether, tied up with political naivete on the part of both Republicans and the British Government, duplicity and downright power mania. Bloody Sunday certainly didn't help matters either.
From my reading of his postings, Fionn is rather better versed in Ulster politics than most here - and certainly more qualified to comment than any other English or Welsh posters in this thread. I also happen to agree with his tongue-in-cheek take on divine intercession! If that makes me sick, well, I'm sick and proud to be. Better a healthy cynicism than a saccharine mawkishness that attempts to sweeten the unpalatable.

And to return to the original subject; praying for peace - as a secular humanist I find the concept of prayer rather pointless, but I do hope and wish for peace, and for the stupidity and mendacity of the Bush and Blair administrations to be recognished by the electorate.