It sounds like an unregistered title (registered in Registry of Deeds rather than Land Registry).
In that situation where the original deeds are lost you need the best available evidence of the deeds - certified copies, and memorials of their registration in the Registry of Deeds. Searches in respect of all parties on title will also be needed.
If the originals are lost, and you're relying on copies, but still want to register the title, it can be gotten around by means of some affidavits as to how they were lost, whether they have been pledged as security for a loan, and either an indemnity indemnifying the state against loss from registering on the basis of the copies (i.e. you take the financial risk) or defective title insurance (a couple of hundred quid).
As to time, well it depends - an investigation of title can take weeks or years depending on the complexity, and how well the solicitor has prepared the case.
The PRA fee is €85, but there will be outlay and solicitors fees which will make it a whole heap more expensive.
If it's registered in the Land Registry and it's a copy folio that's gone missing, don't worry, just get another copy. If it's a land certificate, just sit on it for a while - the problem will go away on 31/12/09 when land certificates are abolished.