Update 6/30: Conquest is now up and running again!
Originally posted by Elrar(Source)
Great news! We’re re-enabling Conquest on all shards right now – we believe the issue was resolved by disabling Corpses in PvP.
We’ve also changed the way rewards are distributed – you’ll now find it more fruitful to capture objectives and win the map then attempting to farm your opponents!
Have fun everyone – and once again a big thanks for all of the patience you’ve demonstrated while we got this squared away, have a wonderful weekend