Some comments on the posts above:-
1.Lack of heirs(Marquess)
The 9th Earl of Kildare(Silken Thomas) rebelled against Henry VIII who had him executed along with his 5 uncles.The heir(later 10th Earl survived but only just and was taken as an infant abroad).When the 1st Duke of Leinster succeeded as Earl of Kildare in 1744 he was the only heir male to the title.
The fate of the peerages rests on Edward Fitzgerald,Lord John's son.If he does not marry and have a son,all the peerages will become extinct.Since the family are the premier dukes,marquesses and earls of Ireland,this would be a loss to the peerage.The successors to the premierships would be respectively,the Duke of Abercorn,the Marquess of Waterford and the Earl of Shrewsbury as Earl of Waterford(assuming the Earldom of Ormonde remains dormant).
The family of Fitzgerald as represented in the gentry would disappear,with the Earldom of Desmond and the three hereditary knightships the Knights of Glin & Kerry and the White Knight all being extinct(the Knight of Kerry is not yet extinct but the present knight has no children and is 75).
2.Other claimants(Marquess)
This claim has been tested before(when the 7th Duke died) and the claimant was unable to prove that his parents(of whom the father was Lord Desmond Fitgerald middle son of the 5th Duke) were married.DNA evidence can have no effect on that controversy.
3.Family finances(Marquess).
Most of the Irish lands(Carton excepted) were sold in the late 19th century and invested and what remains is held by trustees.The 7th Duke sold(while Lord Edward Fitzgerald) his life interest for thirty thousand pounds(which he subsequently wasted) to Sir Henry Mallaby Deeley who enjoyed the income while the 7th Duke was alive.When the 8th Duke succeeded he inherited what was left.The possession of the life interest by a third party however prevented any tax planning,so the estate would have been diminished in size by reason of that fact alone.Carton was sold to Lord Brocket by Sir Henry Mallaby Deeley,but he did so with the consent of the trustees and the proceeds would have remained in the estate,Sir Henry being entitled to the income only.