Are the rings not shown on the left side of the character model, second tab from the top? If you hover the mouse over another ring, do you get a 'currently equipped' comparison of stats?
Were the rings there at first and disappeared later, or did the never actually equip? If you hover the mouse cursor over the ring slots, does the description say 'Empty first/second ring slot'?
Did you equip them by right clicking or drag and dropping in the inventory? If you only tried one do you have another ring to try the other?