Your story, assuming we know all the facts, is shocking, Scooby.
You tried to pay as soon as you could, and were fined when you tried.
I would have thought this was reasonable.
In the UK, posters would be on display in most stations saying that you must buy a ticket before travelling, or where this is not possible, at the first available opportunity, ie a member of staff on board a train, or at your destination etc.
I've looked at the conditions of travel on the Irish rail website, available here:
http://www.irishrail.ie/media/ConditionsOfTravel1.pdf
It was last updated in June 2004.
The only thing I can find says:
Conditions of Carriage of Passengers:
Conditions of Issue of Passenger Tickets
4.4 Where any person travels without a valid ticket, he or she will be required to pay the full ordinary single fare for the journey made and he or she may be liable to prosecution.
No reference whatsoever about their being available facilities to buy a ticket before you travel. Just, you must have one.
So the message is, if you can't buy one, don't travel, because if you do, Irish Rail can prosecute you.
Given this, I'm not sure a solicitor can do much. And I'm sure their fee would quickly clock over the level of the fine.
So I think, on balance, much as I think you have done what is fair and reasonable, and what I would have done in the same circumstances because my knowledge would have been based on experience in the UK (before I'd read the conditions of travel above) I'd pay the fine.
And never, ever travel Irish Rail again without a ticket. Clearly, if you have no other available forms of transport available to you, this is a problem.
In my opinion, it's a pretty bad indictment of Irish Rail though, to fine a passenger that has tried to pay at the first available opportunity. And not to have updated its Conditions of Travel in nearly 9 years.
I hope someone else will be able to say that I'm wrong and you do have a case.