The reason that Social Welfare may not have your records is that DA wasn't always paid by Social Welfare.
Disability Allowance used to be called Disabled Persons Maintenance Allowance (DPMA) and was paid by the Health Boards. I can't remember exactly when it transferred over to SW, but I think it may have been after 2000.
Your claim papers may still be with the local Health Board (HSE) offices.
Edit: The transfer was longer ago than I thought! Claims transferred from the Health Boards to SW in October 1996. If you were on a payment at that stage, it's possible that the claim papers may have remained with the health board.